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Logic gates

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Quick recall · 266 cards
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Why is the binary number system widely used in computer systems?
B · It uses only two digits, 0 and 1, which can be easily represented by electronic switches
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Which of the following is a correct binary addition?
A. 1011 + 1101 = 11000
B. 1011 + 1101 = 10000
C. 1011 + 1101 = 1110
D. 1011 + 1101 = 10010
A · 1011 + 1101 = 11000
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Convert the decimal number 85 to octal.
B · 135
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The decimal number 108 in the octal number system is:
D · 154
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What could be the maximum value of a single digit in an octal number system?
B · 7
Octal (base-8) uses digits 0-7. Maximum single digit is 7. Option B.
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The maximum number of bits sufficient to represent an octal number in binary is _______
B · 3
Octal has 8 digits (2³=8), so 3 bits represent any octal digit in binary. Option B.
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What is the hexadecimal representation of (657)8?
B · 1B9
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Give the hexadecimal value of the 12-bit binary value 000011101001.
A · 0E9
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The logic XOR operation of (4AC0)16 and (B53F)16 results in ________.
A · 7F3F
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Convert the Decimal number 85 to Octal.
A · 135₈
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Convert the binary number 110110₂ to decimal.
C · 54
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Convert the binary number 110001₂ to decimal.
B · 49
To convert binary 110001₂ to decimal, we calculate: 1×2⁵ + 1×2⁴ + 0×2³ + 0×2² + 0×2¹ + 1×2⁰ = 32 + 16 + 0 + 0 + 0 + 1 = 49. Therefore, 110001₂ = 49₁₀, which is option B.
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Convert the binary number 1101110₂ to decimal.
C · 119
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Which among the following is an appropriate binary conversion for the number 421 (which is of base 10)?
D · 110100101
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A man has Rs.480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
D · 96
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The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay?
B · Rs. 2400
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What should come in place of question mark? (34.5 × 14 × 42) ÷ 2.8 = ?
B · 7425
Calculate step by step: First, 34.5 × 14 = 483. Then 483 × 42 = 20286. Finally, 20286 ÷ 2.8 = 7245. Option C is 7245. Wait, source option 3=7245. Verified calculation confirms 7245.
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Which of the following represents the truth table for ~p ∧ q?
B · B. True only when p is false and q is true
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What is the primary use of a Karnaugh Map (K-map) in Boolean algebra?
A · To simplify logic circuits
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What encoding technique is used to assign place values to cells in a Karnaugh Map?
B · Gray code encoding
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Which of the following is the base of the binary number system?
A · 2
The binary number system is base 2, meaning it uses only two digits: 0 and 1.
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What is the binary representation of the decimal number 5?
A · 101
The decimal number 5 is represented as 101 in binary (\(1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 5\)).
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Which of the following binary numbers is equal to decimal 12?
A · 1100
Binary 1100 equals decimal 12 because \(1 \times 2^3 + 1 \times 2^2 + 0 + 0 = 8 + 4 = 12\).
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Convert the octal number 27 to binary.
A · 010111
Octal 27 is converted by converting each digit to 3-bit binary: 2 = 010, 7 = 111, so combined binary is 010111.
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What is the decimal equivalent of the binary number \(110101_2\)?
A · 53
Calculating decimal: \(1\times 2^5 + 1\times 2^4 + 0 + 1\times 2^2 + 0 + 1\times 2^0 = 32 + 16 + 0 + 4 + 0 + 1 = 53\).
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Convert the hexadecimal number \(3F_{16}\) to binary.
A · 00111111
Hex 3 = 0011 and F = 1111, so combined binary is 00111111.
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Convert the decimal number 156 to binary.
A · 10011100
Decimal 156 in binary is 10011100 (\(128 + 16 + 8 + 4 = 156\)).
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What is the result of binary addition \(1011_2 + 1101_2\)?
A · 11000
Adding: 1011 + 1101 = 11000 (decimal 11 + 13 = 24).
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Calculate the binary subtraction: \(11010_2 - 1011_2\).
A · 10011
Decimal equivalent: 26 - 11 = 15, which is 10011 in binary.
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What is the product of binary numbers \(101_2 \times 11_2\)?
A · 1111
Decimal equivalent: 5 × 3 = 15, which is 1111 in binary.
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Perform the binary division: \(1100_2 \div 10_2\). What is the quotient?
A · 110
Decimal equivalent: 12 ÷ 2 = 6, which is 110 in binary.
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What is the result of the bitwise AND operation between \(1011_2\) and \(1101_2\)?
A · 1001
Bitwise AND: 1&1=1, 0&1=0, 1&0=0, 1&1=1, so result is 1001.
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What is the result of the bitwise OR operation between \(1001_2\) and \(0110_2\)?
A · 1111
Bitwise OR: 1|0=1, 0|1=1, 0|1=1, 1|0=1, so result is 1111.
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What is the result of the bitwise XOR operation between \(1100_2\) and \(1010_2\)?
A · 0110
Bitwise XOR: 1^1=0, 1^0=1, 0^1=1, 0^0=0, so result is 0110.
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If the binary number \(101101_2\) is left-shifted by 2 positions, what is the resulting binary number?
B · 10110100
Left shifting by 2 adds two zeros at the right: 10110100.
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Which of the following is NOT an application of binary in computing?
C · Decimal arithmetic
Decimal arithmetic uses base 10, not binary. Binary is used in data representation, logic gates, and memory addressing.
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Why do computers use the binary number system internally?
B · Because electronic circuits have two stable states
Computers use binary because electronic circuits have two stable states (on/off), which correspond naturally to binary digits 0 and 1.
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Which of the following is a direct application of binary logic in computer hardware?
B · Logic gates like AND, OR, NOT
Logic gates implement binary logic operations directly in hardware using binary signals.
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What is the base or radix of the binary number system?
A · 2
The binary number system uses base 2, meaning it has only two digits: 0 and 1.
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Which of the following binary numbers is equivalent to decimal 13?
A · 1101
The binary number 1101 equals \(1\times2^3 + 1\times2^2 + 0\times2^1 + 1\times2^0 = 8 + 4 + 0 + 1 = 13\).
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Which of the following statements about binary numbers is TRUE?
B · Binary numbers use digits 0 and 1 to represent values
Binary numbers use only two digits, 0 and 1, to represent values in base 2.
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Convert the decimal number 45 to binary.
A · 101101
Decimal 45 converted to binary is 101101 (32 + 8 + 4 + 1).
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Refer to the conversion flowchart below. Which step correctly converts the decimal number 14 to binary?
A · Divide 14 by 2, remainder 0, quotient 7
When converting decimal 14 to binary, dividing by 2 gives remainder 0 and quotient 7 initially.
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What is the hexadecimal equivalent of the binary number \(101111\)?
D · 2E
Binary 101111 equals decimal 47, which is 2E in hexadecimal.
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Convert the octal number 57 to binary.
A · 101111
Octal 5 is 101 and 7 is 111 in binary, so 57 octal = 101111 binary.
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What is the result of binary addition \(1101 + 1011\)?
A · 11000
Adding 1101 (13) and 1011 (11) gives 11000 (24) in binary.
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Calculate the result of binary subtraction \(10110 - 1101\).
A · 10001
Binary 10110 (22) minus 1101 (13) equals 10001 (9).
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What is the product of binary numbers \(101\) and \(11\)?
A · 1111
Binary 101 (5) multiplied by 11 (3) equals 1111 (15).
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Refer to the carry diagram below for binary addition of two 4-bit numbers. What is the carry out of the third bit addition?
B · 1
The carry diagram shows a carry generated at the third bit addition, so carry out is 1.
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Which logic gate outputs HIGH only when both inputs are HIGH?
A · AND gate
AND gate outputs HIGH (1) only when both inputs are HIGH (1).
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Refer to the logic gate circuit below. What is the output if inputs A=1 and B=0?
B · 0
The circuit is an AND gate; with inputs 1 and 0, output is 0.
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Which logic gate produces an output of 1 when the number of HIGH inputs is odd?
A · XOR gate
XOR gate outputs 1 when there is an odd number of HIGH inputs.
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Refer to the logic gate circuit below. What Boolean expression does this circuit represent?
B · A AND (B OR C)
The circuit shows an OR gate with inputs B and C feeding into an AND gate with input A, representing A AND (B OR C).
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Which of the following is a common application of binary numbers in computing?
A · Representing colors in digital images
Binary numbers are used to represent colors in digital images by encoding color intensities as binary values.
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How does binary representation facilitate error detection in digital communication?
A · By using parity bits to check for errors
Parity bits are added to binary data to detect errors during transmission by checking if the number of 1s is even or odd.
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Refer to the diagram below illustrating a binary conversion process in a computer system. Which component is responsible for converting analog signals to binary data?
A · Analog-to-Digital Converter (ADC)
The Analog-to-Digital Converter (ADC) converts analog signals into binary data for processing by the computer.
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If a 16-bit binary number X is such that when XORed with its bitwise complement (~X), the result is 65535, which of the following must be true about X?
D · X has all bits set to 1
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Consider two 8-bit binary numbers A and B. If A AND B = 0 and A OR B = 255, which of the following statements is always true?
A · A and B are bitwise complements
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If the binary number 101101101 is interpreted as an unsigned integer and then converted to Gray code, what is the decimal value of the Gray code obtained?
C · 439
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A 13-bit binary number has exactly 6 bits set to 1. If the number is incremented by 1, the number of bits set to 1 becomes 4. Which of the following could be the original number?
D · 8190
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If the 11-bit binary number 10110101101 is rotated right by 4 bits, and then XORed with the original number, the result is a binary number with how many bits set to 1?
D · 8
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A 9-bit binary number N satisfies the condition that N XOR (N left-shifted by 1) equals 511. What is the decimal value of N?
A · 341
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If a 7-bit binary number is such that its two's complement is equal to its bitwise reversal, what is the decimal value of the number?
C · -39
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If the 10-bit binary number 1001110110 is interpreted as an unsigned integer, and then its bits are inverted and incremented by 1, what is the decimal value of the result?
B · 514
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Which of the following 12-bit binary numbers has the property that its bitwise AND with its bitwise left rotation by 7 bits equals zero?
A · 101010101010
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A 16-bit binary number has the property that when XORed with its right rotation by 8 bits, the result is the same as the original number. Which of the following numbers satisfies this property?
D · 0
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Which of the following 8-bit binary numbers has the maximum number of trailing zeros and still remains divisible by 16 when interpreted as an unsigned integer?
D · 11000000
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Which of the following digits is NOT valid in the octal number system?
B · 8
The octal number system uses digits from 0 to 7 only. Digit 8 is invalid.
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What is the base (radix) of the octal number system?
B · 8
The octal number system is base 8, meaning it uses digits 0 through 7.
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In the octal number 345, what is the place value of digit '4'?
C · 8
In octal, place values are powers of 8. The digit '4' is in the 8¹ place, so its place value is 8.
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Convert the octal number \(127_8\) to its decimal equivalent.
A · 87
Calculate decimal: \(1 \times 8^2 + 2 \times 8^1 + 7 \times 8^0 = 64 + 16 + 7 = 87\). So correct answer is 87.
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What is the binary equivalent of the octal number \(53_8\)?
A · 101011
Convert each octal digit to 3-bit binary: 5 = 101, 3 = 011. So binary is 101011.
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Convert the decimal number 100 to octal.
A · 144
Divide 100 by 8: 100 ÷ 8 = 12 remainder 4, 12 ÷ 8 = 1 remainder 4, 1 ÷ 8 = 0 remainder 1. So octal is 144.
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Convert the hexadecimal number \(2F_{16}\) to octal.
D · 157
Hex 2F = binary 0010 1111. Group into 3 bits from right: 000 101 111 = octal 157.
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What is the sum of octal numbers \(27_8 + 35_8\)?
D · 62_8
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Perform the octal subtraction: \(75_8 - 46_8\). What is the result?
A · 27_8
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Add the octal numbers \(156_8 + 47_8\). What is the result in octal?
D · 213_8
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Why was the octal number system historically important in computing?
B · Because each octal digit corresponds exactly to three binary digits
Each octal digit corresponds to exactly three binary digits, making it easier to represent binary data compactly and readably.
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Which of the following is a common application of the octal number system in computing?
A · Representing memory addresses in early computer systems
Octal was commonly used to represent memory addresses and machine instructions in early computers due to its compactness and easy conversion to binary.
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Which statement best explains why octal is less commonly used today compared to hexadecimal?
A · Hexadecimal digits correspond to four binary bits, making it more efficient
Hexadecimal digits correspond exactly to four binary bits, which aligns better with modern byte sizes (8, 16, 32 bits), making it more efficient and widely used.
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Which of the following digits is NOT valid in the octal number system?
B · 8
The octal number system uses digits from 0 to 7 only. Digit 8 is invalid in octal.
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What is the base of the octal number system?
B · 8
The octal number system is base 8, meaning it uses digits from 0 to 7.
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Which octal number represents the decimal number 15?
A · 17
Decimal 15 in octal is calculated as \(1 \times 8 + 7 = 15\).
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What is the decimal equivalent of the octal number \(345_8\)?
A · 229
Convert \(345_8\) to decimal: \(3 \times 8^2 + 4 \times 8^1 + 5 \times 8^0 = 192 + 32 + 5 = 229\).
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Convert the binary number \(101101_2\) to octal.
B · 65
Group binary digits in 3s from right: 101 101. Convert each group: 101 = 5, 101 = 5. So octal is \(65_8\).
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Which hexadecimal number corresponds to the octal number \(127_8\)?
A · 57
Convert octal \(127_8\) to decimal: \(1 \times 64 + 2 \times 8 + 7 = 64 + 16 + 7 = 87\). Decimal 87 in hex is \(57_{16}\). But options show 4F which is 79 decimal, so correct is 57.
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Convert the decimal number 255 to octal.
A · 377
Divide 255 by 8 repeatedly: 255/8=31 remainder 7, 31/8=3 remainder 7, 3/8=0 remainder 3. So octal is \(377_8\).
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What is the result of octal addition \(45_8 + 32_8\)?
A · 77_8
Convert to decimal: 45_8 = 37 decimal, 32_8 = 26 decimal. Sum = 63 decimal. Convert back to octal: 63/8=7 remainder 7 → 77_8.
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Calculate the octal subtraction \(123_8 - 57_8\).
C · 44_8
Convert to decimal: 123_8 = 83 decimal, 57_8 = 47 decimal. Difference = 36 decimal. Convert 36 to octal: 44_8.
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Find the product of \(7_8 \times 6_8\) in octal.
A · 52_8
Convert to decimal: 7_8 = 7 decimal, 6_8 = 6 decimal. Product = 42 decimal. Convert 42 to octal: 42/8=5 remainder 2 → 52_8.
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Which of the following is a common application of the octal number system?
B · Simplifying binary representation in computing
Octal is used to simplify binary representation because each octal digit corresponds exactly to three binary digits.
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Which property of octal numbers makes them useful in digital systems?
C · Each octal digit maps to exactly three binary bits
Each octal digit corresponds to exactly three binary bits, making conversions between binary and octal straightforward.
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In a computer system, which of the following is a reason octal numbers were historically preferred over hexadecimal?
A · Octal digits correspond to 3 bits, matching early 12-bit and 24-bit architectures
Early computer architectures used word lengths divisible by 3 (like 12, 24 bits), making octal (3 bits per digit) a natural fit for grouping bits.
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Given two octal numbers A = 7362₈ and B = 4527₈, find the remainder when the product A × B is divided by 512₈. Note: 512₈ is an octal number. Choose the correct remainder in octal.
C · 1763₈
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Match the following octal numbers with their equivalent binary representations: Column A: 1) 3457₈ 2) 1276₈ 3) 6543₈ 4) 7012₈ Column B: A) 111 010 111 111₂ B) 001 010 111 110₂ C) 110 101 100 011₂ D) 111 000 001 010₂
A · 1-A, 2-B, 3-C, 4-D
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If the octal number X satisfies the equation (X + 1234₈) × 7₈ = 76543₈, find the value of X in octal.
C · 6325₈
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Find the number of octal numbers between 1000₈ and 7777₈ (inclusive) whose digit sum in octal is equal to 15₈.
B · 105
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Which of the following octal numbers is a perfect square in decimal and also has an octal digit sum equal to 10₈?
A · 144₈
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Consider the octal number N = ABCD₈ where A, B, C, D are octal digits. If N is divisible by 11₈ and the sum of digits is 20₈, which of the following could be N?
B · 3617₈
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If the octal number 1ABC₈ is such that when converted to decimal, it is divisible by 13 decimal and the digit sum in octal is 21₈, find the possible value of ABC (each digit octal) given options.
B · 276
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Which of the following octal numbers, when multiplied by 5₈, results in a number whose last three digits in octal are 000?
B · 2560₈
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If the octal number 123456₈ is represented in base 4, what is the sum of its digits in base 4?
B · 221
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Which of the following octal numbers is equal to its reverse when converted to decimal?
B · 12321₈
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If the octal number 765432₈ is divided by 11₈, what is the remainder in octal?
A · 7₈
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Find the octal number X such that when added to 765₈ and then multiplied by 3₈, the result is 5432₈.
A · 123₈
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Match the octal number with its equivalent hexadecimal number: Column A: 1) 765₈ 2) 1234₈ 3) 5670₈ 4) 4321₈ Column B: A) 1F5₁₆ B) 29C₁₆ C) 17C8₁₆ D) 11A1₁₆
A · 1-A, 2-B, 3-C, 4-D
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If the octal number 34567₈ is expressed in binary, what is the parity (even or odd) of the number of 1's in its binary representation?
A · Even
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Which of the following octal numbers is divisible by both 7₈ and 11₈?
C · 231₈
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Which of the following digits is NOT valid in the hexadecimal number system?
C · G
Hexadecimal digits range from 0 to 9 and A to F. 'G' is not a valid hexadecimal digit.
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What is the base of the hexadecimal number system?
D · 16
Hexadecimal is a base-16 number system, using sixteen distinct symbols.
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How many bits are represented by one hexadecimal digit?
C · 4
One hexadecimal digit corresponds exactly to 4 binary bits.
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What is the binary equivalent of hexadecimal digit \( \text{A} \)?
A · 1010
Hexadecimal A corresponds to decimal 10, which is binary 1010.
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Convert hexadecimal number \( 2F \) to binary.
A · 00101111
2 in hex is 0010 and F is 1111, so combined binary is 00101111.
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What is the binary equivalent of hexadecimal number \( 3C7 \)?
A · 001111000111
3 = 0011, C = 1100, 7 = 0111, so combined binary is 001111000111.
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Convert hexadecimal \( 9D4 \) to binary.
A · 100111010100
9 = 1001, D = 1101, 4 = 0100, combined binary is 100111010100.
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What is the hexadecimal equivalent of binary number \( 11110010 \)?
A · F2
Binary 1111 is F and 0010 is 2, so hexadecimal is F2.
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Convert binary \( 10110111 \) to hexadecimal.
A · B7
1011 is B and 0111 is 7, so hexadecimal is B7.
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What is the hexadecimal equivalent of binary number \( 110111101001 \)?
A · DE9
1101 = D, 1110 = E, 1001 = 9, so hexadecimal is DE9.
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Convert binary \( 100111011101 \) to hexadecimal.
A · 9DD
1001 = 9, 1101 = D, 1101 = D, so hexadecimal is 9DD.
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What is the hexadecimal equivalent of binary number \( 111010111010 \)?
A · EBA
1110 = E, 1011 = B, 1010 = A, so hexadecimal is EBA.
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What is the decimal equivalent of hexadecimal number \( 1A \)?
A · 26
1A in hex = (1 \times 16) + (10) = 26 decimal.
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Convert hexadecimal \( 3F \) to decimal.
A · 63
3F = (3 \times 16) + 15 = 48 + 15 = 63 decimal.
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What is the decimal equivalent of hexadecimal number \( 7B2 \)?
A · 1970
7B2 = (7 \times 256) + (11 \times 16) + 2 = 1792 + 176 + 2 = 1970.
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Convert hexadecimal \( 2E9 \) to decimal.
A · 745
2E9 = (2 \times 256) + (14 \times 16) + 9 = 512 + 224 + 9 = 745.
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What is the decimal equivalent of hexadecimal number \( F3A \)?
A · 3898
F3A = (15 \times 256) + (3 \times 16) + 10 = 3840 + 48 + 10 = 3898.
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What is the hexadecimal equivalent of decimal number \( 45 \)?
A · 2D
45 divided by 16 is 2 remainder 13 (D), so hexadecimal is 2D.
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Convert decimal number \( 120 \) to hexadecimal.
A · 78
120 divided by 16 is 7 remainder 8, so hexadecimal is 78.
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Convert decimal \( 350 \) to hexadecimal.
A · 15E
350 divided by 16 is 21 remainder 14 (E), 21 decimal is 15 hex, so 15E.
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Convert decimal \( 1023 \) to hexadecimal.
A · 3FF
1023 decimal is 3FF in hexadecimal.
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Convert decimal \( 2047 \) to hexadecimal.
A · 7FF
2047 decimal is 7FF in hexadecimal.
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What is the sum of hexadecimal numbers \( A5 \) and \( 3C \)?
A · E1
A5 (165 decimal) + 3C (60 decimal) = 225 decimal = E1 hex.
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Calculate \( 1F + 2B \) in hexadecimal.
A · 4A
1F (31 decimal) + 2B (43 decimal) = 74 decimal = 4A hex.
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Subtract hexadecimal \( 7A \) from \( C3 \). What is the result?
A · 49
C3 (195 decimal) - 7A (122 decimal) = 73 decimal = 49 hex, but 49 hex is 73 decimal. The correct hex is 49, so option A is correct.
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Multiply hexadecimal \( 6 \) by \( 9 \). What is the product in hexadecimal?
A · 36
6 (decimal 6) × 9 (decimal 9) = 54 decimal = 36 hex.
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Divide hexadecimal \( B8 \) by \( 4 \). What is the quotient in hexadecimal?
A · 2E
B8 hex = 184 decimal; 184 ÷ 4 = 46 decimal = 2E hex.
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What is the result of hexadecimal addition \( FF + 1 \)?
A · 100
FF hex is 255 decimal; 255 + 1 = 256 decimal = 100 hex.
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Which of the following is a common application of hexadecimal in computing?
A · Memory addressing
Hexadecimal is widely used for memory addressing due to its compact representation of binary data.
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Why is hexadecimal preferred over binary in representing memory addresses?
B · It is more compact and readable
Hexadecimal is more compact and easier for humans to read compared to long binary strings.
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Which of the following is an example of hexadecimal use in color representation?
A · #FF5733
Hexadecimal color codes like #FF5733 represent colors in web design.
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Which of the following is NOT a typical application of hexadecimal in computing?
C · Audio file encoding
Audio file encoding typically uses formats like PCM or compressed formats, not hexadecimal directly.
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What does the hexadecimal number \( 0x1A3F \) typically represent in computing?
A · A memory address
Hexadecimal numbers prefixed with 0x often represent memory addresses in computing.
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In the context of data representation, what does the hexadecimal number \( FF \) represent when used in memory addressing?
A · The highest value of one byte
FF hex corresponds to 255 decimal, the maximum value for an 8-bit byte.
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Which of the following hexadecimal values is commonly used to represent the color white in RGB hex color codes?
A · #FFFFFF
#FFFFFF represents white color in RGB hexadecimal notation.
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In a 32-bit memory address, how many hexadecimal digits are required to represent the address fully?
A · 8
Each hex digit represents 4 bits, so 32 bits require 8 hex digits.
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Which hexadecimal value represents the color blue in RGB hex color codes?
A · #0000FF
#0000FF represents blue color in RGB hexadecimal notation.
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Which of the following hexadecimal numbers correctly represents the binary number \( 10101111 \)?
A · AF
1010 is A and 1111 is F, so the hex equivalent is AF.
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Which of the following digits is NOT valid in the hexadecimal number system?
C · G
Hexadecimal digits include 0-9 and A-F. 'G' is not a valid hexadecimal digit.
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What is the base (radix) of the hexadecimal number system?
D · 16
Hexadecimal is a base-16 number system, using sixteen distinct symbols.
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What is the decimal equivalent of the hexadecimal digit 'A'?
A · 10
In hexadecimal, 'A' represents the decimal value 10.
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Which of the following hexadecimal numbers is the smallest?
C · 0x0A
0x0A (decimal 10) is smaller than 0x10 (16), 0x1F (31), and 0x2B (43).
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In the hexadecimal system, what is the value of the digit 'F' in decimal?
B · 15
'F' in hexadecimal corresponds to 15 in decimal.
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Which of the following correctly represents the hexadecimal number system?
A · Uses digits 0-9 and letters A-F with base 16
Hexadecimal uses digits 0-9 and letters A-F and is base 16.
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Convert the hexadecimal number \( \text{2F} \) to its decimal equivalent.
A · 47
\( 2F_{16} = 2 \times 16 + 15 = 32 + 15 = 47 \) in decimal.
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What is the binary equivalent of the hexadecimal number \( \text{9C} \)?
A · 10011100
9 in hex is 1001 and C is 1100, so \( 9C_{16} = 10011100_2 \).
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Convert the decimal number 255 to hexadecimal.
A · FF
255 decimal is \( 15 \times 16 + 15 = FF_{16} \).
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What is the octal equivalent of the hexadecimal number \( \text{3E} \)?
A · 76
\( 3E_{16} = 0011 1110_2 \). Grouping binary into 3 bits: 011 111 0 (add leading zero) = 076 octal.
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Convert the binary number \( 11010110_2 \) to hexadecimal.
A · D6
Split into 4-bit groups: 1101 (D) and 0110 (6), so \( 11010110_2 = D6_{16} \).
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What is the decimal equivalent of the hexadecimal number \( \text{1A3} \)?
A · 419
\( 1A3_{16} = 1 \times 256 + 10 \times 16 + 3 = 256 + 160 + 3 = 419 \).
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Add the hexadecimal numbers \( \text{3B} + \text{4E} \). What is the result in hexadecimal?
D · 7D
\( 3B_{16} = 59_{10}, 4E_{16} = 78_{10} \). Sum = 137 decimal = 7D hex.
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Subtract \( \text{2A} \) from \( \text{5F} \) in hexadecimal. What is the result?
A · 35
\( 5F_{16} = 95_{10}, 2A_{16} = 42_{10} \). Difference = 53 decimal = 35 hex.
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What is the result of \( \text{A} + \text{5} \) in hexadecimal?
A · F
A (10 decimal) + 5 = 15 decimal = F hex.
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Calculate the hexadecimal sum: \( \text{1C} + \text{2F} + \text{3A} \).
B · 8B
\( 1C = 28, 2F = 47, 3A = 58 \). Sum = 133 decimal = 8B hex.
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What is the result of subtracting \( \text{1E} \) from \( \text{3C} \) in hexadecimal?
B · 1C
\( 3C = 60, 1E = 30 \). Difference = 30 decimal = 1C hex.
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Which of the following is a common application of hexadecimal in computing?
A · Representing memory addresses
Hexadecimal is widely used to represent memory addresses due to its compactness and alignment with binary.
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Why is hexadecimal preferred over binary for representing machine-level data?
A · Hexadecimal is easier to read and shorter than binary
Hexadecimal condenses binary data into fewer digits, making it easier for humans to read and interpret.
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Which of the following is an example of a hexadecimal color code used in web design?
A · #FF5733
Hex color codes start with '#' followed by six hexadecimal digits representing RGB values.
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Which of the following hexadecimal numbers is most likely a valid memory address in a 16-bit system?
A · 0x1A3F
0x1A3F is a valid 16-bit hexadecimal address; others contain invalid characters or exceed 16 bits.
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In computing, the hexadecimal value \( \text{0xFF} \) often represents which of the following?
A · Maximum value for an 8-bit byte
\( 0xFF \) equals 255 decimal, the maximum value for an 8-bit byte.
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Which hexadecimal number represents the binary pattern \( 1010\ 1100\ 1111\ 0001 \)?
A · ACF1
Each 4-bit group corresponds to a hex digit: 1010 (A), 1100 (C), 1111 (F), 0001 (1).
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What is the hexadecimal representation of the 16-bit memory address \( 0001\ 1010\ 1111\ 0101_2 \)?
A · 1AF5
Group bits into 4: 0001 (1), 1010 (A), 1111 (F), 0101 (5) = 1AF5 hex.
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Which of the following hexadecimal values is valid for a 12-bit memory address?
A · 0xFFF
12 bits correspond to 3 hex digits; 0xFFF is the maximum 12-bit hex value.
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If a memory address is represented as \( \text{0x3E7} \), what is its decimal equivalent?
A · 999
\( 3 \times 256 + 14 \times 16 + 7 = 768 + 224 + 7 = 999 \).
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Which logical operation is easiest to perform directly on hexadecimal numbers without converting to binary?
C · Bitwise NOT
Bitwise NOT can be performed digit-wise by replacing each hex digit with its complement (F - digit).
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What is the result of the bitwise AND operation between \( \text{0x9F} \) and \( \text{0xF1} \)?
A · 0x91
\( 0x9F = 10011111_2 \), \( 0xF1 = 11110001_2 \). AND = 10010001 = 0x91.
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Which hexadecimal number results from the bitwise OR of \( \text{0x3C} \) and \( \text{0xA7} \)?
A · 0xBF
\( 0x3C = 00111100_2 \), \( 0xA7 = 10100111_2 \). OR = 10111111 = 0xBF.
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In error detection, which hexadecimal value is commonly used as a parity mask for 8-bit data?
A · 0xFF
0xFF (all bits set) is often used as a mask in parity and error detection schemes.
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What is the hexadecimal result of XOR operation between \( \text{0x5A} \) and \( \text{0x3F} \)?
A · 0x65
\( 0x5A = 01011010_2 \), \( 0x3F = 00111111_2 \). XOR = 01100101 = 0x65.
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Which of the following hexadecimal values represents an error detection code with a single bit error capability in a 4-bit data system?
C · 0x5
0x5 (0101) is a common parity pattern used in Hamming codes for single-bit error detection in 4-bit data.
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If the hexadecimal number 0xABCDE is incremented by 1, and then bitwise ANDed with 0xFFF0F, what is the hexadecimal result?
A · 0xABCD0
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Consider the hexadecimal number 0x1A3F5. If you extract the 3rd nibble from the right (0-based indexing) and multiply it by the decimal equivalent of the least significant nibble, what is the result in decimal?
C · 75
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If the hexadecimal number 0x7E3B9 is represented in binary and then rotated right by 7 bits, what is the hexadecimal equivalent of the resulting binary number?
B · 0xF9E7C
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Which of the following hexadecimal numbers, when added to 0xFFFFF, results in a hexadecimal number whose least significant byte is 0x00?
A · 0x00001
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Given two hexadecimal numbers X = 0x1C3F and Y = 0x2A7B, compute ((X AND Y) OR (X XOR Y)) in hexadecimal.
B · 0x3C7F
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If a hexadecimal number N satisfies the condition that N XOR 0xFFFF equals the bitwise NOT of N, which of the following could be N?
A · 0x1234
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Consider the hexadecimal number 0xDEADBEEF. If you split it into two 16-bit halves and swap them, then add 0x1234 to the result, what is the final hexadecimal number?
C · 0xBEEFDEAD + 0x1234 = 0xBEF00F01
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If a hexadecimal number N satisfies the equation N + (N XOR 0xFFFF) = 0xFFFF, what is the decimal value of N?
A · 32767
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Which hexadecimal number, when multiplied by 0x10 and then added to 0xF, results in 0x1A3F?
B · 0x19
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If the hexadecimal number 0xABCDE is ANDed with 0x0F0F0, then ORed with 0x12345, what is the final hexadecimal number?
B · 0x1B3F5
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Which of the following hexadecimal numbers is a palindrome when represented in binary (considering full 16-bit representation)?
D · 0x5A5A
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If the hexadecimal number 0x123456 is right shifted by 8 bits and then XORed with 0xABCD, what is the resulting hexadecimal number?
A · 0xB9F9
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Which hexadecimal number, when added to its own bitwise complement (with respect to 16 bits), results in 0xFFFF?
A · Any 16-bit number
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Which of the following is the base of the decimal number system?
C · 10
The decimal number system is base 10, meaning it uses digits from 0 to 9.
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In which number system is the digit 'F' used?
D · Hexadecimal
'F' is a valid digit in the hexadecimal system representing decimal 15.
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What is the decimal equivalent of the binary number \(1011_2\)?
C · 11
The binary number \(1011_2\) equals \(1\times2^3 + 0\times2^2 + 1\times2^1 + 1\times2^0 = 8 + 0 + 2 + 1 = 11\).
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Convert the decimal number 45 to its binary equivalent.
A · 101101
45 in decimal is \(32 + 8 + 4 + 1 = 101101_2\).
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What is the octal equivalent of the binary number \(110101_2\)?
A · 65
Grouping binary digits in threes from right: 110 101 = 6 5 in octal, so answer is 65. However, 110101 binary is 53 decimal, which is 65 octal. So correct answer is 65.
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Convert the hexadecimal number \(2F_{16}\) to decimal.
A · 47
\(2F_{16} = 2 \times 16 + 15 = 32 + 15 = 47\) in decimal.
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Which of the following is the correct binary representation of decimal 100?
A · 1100100
Decimal 100 equals \(64 + 32 + 4 = 1100100_2\).
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Convert the decimal number 255 to hexadecimal.
A · FF
255 decimal equals \(15 \times 16 + 15 = FF_{16}\).
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What is the result of binary addition \(1011_2 + 1101_2\)?
A · 11000
\(1011_2 = 11_{10}, 1101_2 = 13_{10}\); sum is 24 decimal which is \(11000_2\).
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What is the 2's complement of the binary number \(0101_2\)?
A · 1011
1's complement of 0101 is 1010; adding 1 gives 1011. But 2's complement is 1011, so correct answer is A.
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Perform the binary subtraction \(10110_2 - 1101_2\). What is the result in binary?
D · 10011
\(10110_2 = 22_{10}, 1101_2 = 13_{10}\); subtraction is 9 decimal which is \(10011_2\).
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Which logic gate outputs 1 only when both inputs are 1?
B · AND
The AND gate outputs 1 only when both inputs are 1.
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Why is hexadecimal representation preferred in computing over binary?
A · It uses fewer digits to represent the same value
Hexadecimal condenses binary data into fewer digits, making it easier for humans to read and write.
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In memory addressing, why are addresses often represented in hexadecimal?
A · Because hexadecimal addresses are shorter and easier to read
Hexadecimal notation shortens long binary addresses, making them easier for programmers to read and debug.
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A computer system uses 12-bit addressing. What is the maximum number of unique memory locations it can address?
B · 4096
With 12 bits, the number of unique addresses is \(2^{12} = 4096\).
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Which of the following correctly defines a number system?
A · A set of symbols and rules to represent numbers in different bases
A number system is a set of symbols and rules used to represent numbers in various bases such as binary, octal, decimal, and hexadecimal.
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What is the base of the hexadecimal number system?
D · 16
The hexadecimal number system is base 16, using digits 0-9 and letters A-F to represent values 10 to 15.
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Which of the following is the correct decimal equivalent of binary number \(101101_2\)?
A · 45
Binary \(101101_2 = 1\times2^5 + 0\times2^4 + 1\times2^3 + 1\times2^2 + 0\times2^1 + 1\times2^0 = 32 + 0 + 8 + 4 + 0 + 1 = 45\). The correct decimal is 45.
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Convert the decimal number 156 to its equivalent hexadecimal representation.
A · 9C
156 divided by 16 gives quotient 9 and remainder 12. Remainder 12 corresponds to C in hex. So, decimal 156 = 9C in hexadecimal.
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Which of the following is the correct octal equivalent of binary number \(110101_2\)?
A · 65
Group binary digits in sets of 3 from right: 110 101. 110 in octal is 6, 101 is 5, so octal is 65.
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What is the binary equivalent of hexadecimal number \(3F_{16}\)?
A · 00111111
Hex 3 = 0011, F = 1111, combined binary is 00111111.
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Convert the octal number \(725_8\) to its decimal equivalent.
A · 469
Decimal = 7\times8^2 + 2\times8^1 + 5\times8^0 = 448 + 16 + 5 = 469.
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Which of the following represents the 2's complement of the 8-bit binary number \(00011010_2\)?
A · 11100110
1's complement of 00011010 is 11100101, adding 1 gives 11100110 which is 2's complement.
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How do you convert a negative decimal number to its signed magnitude binary representation?
A · Convert the magnitude to binary and set the leftmost bit to 1
Signed magnitude representation uses the leftmost bit as sign bit (1 for negative), rest bits represent magnitude.
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What is the 2's complement of the decimal number -25 in 8-bit binary?
A · 11100111
25 in binary is 00011001. 1's complement is 11100110, adding 1 gives 11100111. But careful calculation shows 11100111 corresponds to -25 in 2's complement. So correct answer is 11100111.
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Which algorithm is commonly used to convert a decimal number to binary?
A · Repeated division by 2 and collecting remainders
Decimal to binary conversion uses repeated division by 2, collecting the remainders from bottom to top as binary digits.
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In the algorithm for converting binary to decimal, what is the main operation performed?
A · Multiplying each bit by \(2^{position}\) and summing
Binary to decimal conversion involves multiplying each bit by \(2^{position}\) (position counted from right starting at 0) and summing all results.
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Which of the following best describes the process of converting a decimal fraction to binary using an algorithm?
A · Multiply the fractional part by 2 repeatedly and record the integer parts
To convert decimal fractions to binary, multiply the fractional part by 2 repeatedly and note the integer parts as binary digits.
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Which of the following is the correct symbol for the AND gate?
A · A semicircle with two inputs on the left and one output on the right
The AND gate is represented by a D-shaped symbol (a semicircle) with two or more inputs on the left and one output on the right.
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What is the symbol for the OR gate?
A · A curved shape with two inputs converging to a pointed output
The OR gate symbol is a curved shape with two inputs converging to a pointed output, resembling a shield or rocket shape.
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Which logic gate is represented by a triangle with a small circle at the output?
A · NOT gate
The NOT gate is symbolized by a triangle pointing right with a small circle (inversion bubble) at the output.
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Which of the following is the truth table output for an AND gate when inputs are A=1 and B=0?
A · 0
The AND gate outputs 1 only when both inputs are 1. For A=1 and B=0, output is 0.
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Refer to the truth table below for a logic gate with inputs A and B and output Q. Which gate does this truth table represent?

ABQ
001
011
101
110
A · NAND gate
The output is 0 only when both inputs are 1, which is the characteristic of a NAND gate.
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Refer to the truth table below. Which logic gate does it represent?

ABQ
000
011
101
111
A · OR gate
The output is 1 when either or both inputs are 1, which matches the OR gate truth table.
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Refer to the truth table below. Identify the logic gate.

ABQ
000
011
101
110
A · XOR gate
The output is 1 when inputs differ and 0 when inputs are the same, which defines the XOR gate.
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Simplify the Boolean expression \( A \cdot \overline{A} + B \cdot 1 \).
A · \( B \)
Since \( A \cdot \overline{A} = 0 \) and \( B \cdot 1 = B \), the expression simplifies to \( 0 + B = B \).
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Simplify the Boolean expression \( (A + B)(A + \overline{B}) \).
A · \( A \)
Expanding: \( (A + B)(A + \overline{B}) = A + B \cdot A + A \cdot \overline{B} + B \cdot \overline{B} = A + AB + A\overline{B} + 0 = A + A(B + \overline{B}) = A + A \cdot 1 = A \).
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Simplify the Boolean expression \( \overline{A + B} + A \cdot B \).
A · \( 1 \)
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Simplify the Boolean expression \( (A + \overline{B})(\overline{A} + B) \).
A · \( A \oplus B \) (XOR gate)
The expression represents the XOR function, which outputs 1 when inputs differ.
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Refer to the combinational logic circuit below. What is the Boolean expression for the output Q?

A B C Q
A · \( (A \cdot B) + C \)
The first gate is an AND gate with inputs A and B, outputting \( A \cdot B \). The output feeds into an OR gate with input C, so output Q = \( (A \cdot B) + C \).
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In the combinational circuit shown below, what is the output expression?

A B C Q
A · \( (A \cdot B) \cdot C \)
The first gate is AND with inputs A and B, outputting \( A \cdot B \). The second gate is AND with inputs \( A \cdot B \) and C, so output Q = \( (A \cdot B) \cdot C \).
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In a combinational logic circuit, the output Q is given by \( \overline{(A \cdot B)} \). Which gate can implement this function directly?
A · NAND gate
The NAND gate outputs the complement of the AND operation, i.e., \( \overline{A \cdot B} \), so it directly implements the function.
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Which of the following gates is considered a universal gate because any logic function can be implemented using only that gate?
A · NAND gate
NAND gates are universal gates because any Boolean function can be implemented using only NAND gates.
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Refer to the diagram below of a logic circuit made only of NAND gates. What is the equivalent logic gate of the circuit?

A A Q
A · NOT gate
The circuit uses a NAND gate with both inputs tied together, which acts as a NOT gate (inverter).
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Which of the following is true about NOR gates as universal gates?
A · Any logic function can be implemented using only NOR gates
NOR gates are universal gates because any Boolean function can be implemented using only NOR gates.
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Refer to the logic circuit below used in a digital system. What is the primary application of this circuit?

Input 1 Input 2 Input 3 Output Q
A · Implementing a majority voter circuit
The circuit combines AND and OR gates to output 1 when the majority of inputs are 1, typical of a majority voter circuit.
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Which logic gate combination is commonly used to implement a half-adder circuit?
A · XOR gate and AND gate
A half-adder uses an XOR gate to produce the sum and an AND gate to produce the carry output.
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Refer to the circuit below. What is the output expression Q?

A B Q
A · \( \overline{A \cdot B} \) (NAND gate output)
The first gate is an AND gate with inputs A and B, outputting \( A \cdot B \). The output feeds into a NOT gate (circle), so output Q = \( \overline{A \cdot B} \).
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Which of the following Boolean expressions can be implemented using only NAND gates?
D · All of the above
NAND gates are universal gates and can be combined to implement any Boolean function including OR, AND, and NOT operations.
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Which logic gate is used in the construction of a multiplexer to select one input from multiple inputs?
A · AND gate
AND gates are used with selection lines to enable one input at a time in a multiplexer.
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Refer to the Boolean simplification steps shown below. What is the simplified form of the expression?

StepExpression
1\( A \cdot (A + B) \)
2\( A \cdot 1 \)
3\( A \)
A · \( A \)
Using the absorption law, \( A \cdot (A + B) = A \cdot 1 = A \).
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Which logic gate output is high only when all inputs are low?
A · NOR gate
The NOR gate outputs 1 only when all inputs are 0 (low).
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Which of the following is a fundamental postulate of Boolean algebra?
A · A + 0 = A
In Boolean algebra, the identity law states that A + 0 = A, meaning OR with 0 leaves the variable unchanged.
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In Boolean algebra, what is the complement of the variable \( A \)?
A · \( \overline{A} \)
The complement of a Boolean variable \( A \) is denoted as \( \overline{A} \), representing NOT A.
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Which of the following expressions is equivalent to \( (A + B)(A + \overline{B}) \)?
A · A
Using distribution and complementarity, \( (A + B)(A + \overline{B}) = A + B\times \overline{B} = A + 0 = A \).
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Which Boolean law states that \( A + A = A \)?
A · Idempotent Law
The Idempotent Law states that OR or AND of a variable with itself results in the variable itself, e.g., \( A + A = A \).
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Using Boolean laws, simplify the expression \( A \times (A + B) \).
A · A
Using the Absorption Law, \( A \times (A + B) = A \).
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Which theorem is represented by the equation \( \overline{A + B} = \overline{A} \times \overline{B} \)?
A · De Morgan's Theorem
De Morgan's Theorem states that the complement of a sum is the product of the complements.
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Simplify the Boolean expression \( (A + B)(A + \overline{B})(\overline{A} + B) \).
C · B
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Which algebraic technique is used to simplify \( AB + A\overline{B} \) to a simpler expression?
B · Distributive Law
Using Distributive Law: \( AB + A\overline{B} = A(B + \overline{B}) = A \times 1 = A \).
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Simplify the expression \( (A + B)(\overline{A} + B) \) using Boolean algebra.
B · A + B
Expanding: \( (A + B)(\overline{A} + B) = A\overline{A} + AB + B\overline{A} + B^2 = 0 + AB + B\overline{A} + B = B + AB + B\overline{A} = B + A(B + \overline{B}) = B + A(1) = A + B \).
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Which of the following is the simplified form of \( A\overline{B} + \overline{A}B + AB \)?
A · A + B
The expression covers all cases except when both are zero, so it simplifies to \( A + B \).
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Refer to the Karnaugh map below for variables A, B, and C. What is the simplified Boolean expression for the minterms marked 1?

AB C 0 1 1 1 0 1
A · B + AC
The K-map grouping covers cells where B=1 or A=1 and C=1, simplifying to \( B + AC \).
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Refer to the Karnaugh map below for variables A, B, and C. Which group of 1s forms the largest implicant for simplification?

AB C 1 1 0 1 0 1
B · Group of two 1s in the top row
The largest group of adjacent 1s is the two cells in the top row, which can be grouped for simplification.
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Refer to the Karnaugh map below. What is the simplified expression considering the 'Don't Care' conditions (marked as X)?

AB C 1 X 0 1 0 1
A · A + C
The 'Don't Care' condition (X) can be considered as 1 to form larger groups, simplifying the expression to \( A + C \).
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Refer to the Karnaugh map below with 'Don't Care' conditions (X). Which of the following is the correct simplified expression?

AB C 1 X X 0 0 1
B · \overline{A} + C
Using 'Don't Care' conditions to form larger groups, the expression simplifies to \( \overline{A} + C \).
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Refer to the Karnaugh map below. What is the minimal expression for the function considering the 'Don't Care' states?

AB C X 1 1 X 0 1
B · B + C
Using 'Don't Care' conditions to form groups, the function simplifies to \( B + C \).
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Refer to the logic circuit diagram below. Which Boolean expression corresponds to the circuit?

A B C AND OR
A · \( (A \times B) + \overline{C} \)
The circuit shows an AND gate with inputs A and B, and a NOT gate on input C feeding into an OR gate combining both outputs, so expression is \( (A \times B) + \overline{C} \).
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Refer to the truth table below. Which simplified Boolean expression corresponds to the output column?

ABCOutput
0000
0011
0101
0111
1000
1011
1100
1111
A · \( B + AC \)
From the truth table, the output is 1 when B=1 or when A=1 and C=1, so simplified expression is \( B + AC \).
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Which of the following is the main advantage of simplifying Boolean expressions in digital circuit design?
A · Reduces the number of logic gates and connections
Simplification reduces the number of gates and interconnections, leading to cost-effective and faster circuits.
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Refer to the logic circuit diagram below. What is the simplified Boolean expression for the circuit?

A B OR AND
A · \( (A + B) \times \overline{B} \)
The circuit shows an OR gate with inputs A and B, feeding an AND gate with NOT B, so expression is \( (A + B) \times \overline{B} \).
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Which Boolean expression represents the minimal form of the function with minterms 1,3,7 and don't care conditions at 2 and 6 for variables A, B, C?

Minterms: 1(001), 3(011), 7(111)
Don't Care: 2(010), 6(110)
A · \( B \times C \)
Including don't care minterms 2 and 6 allows grouping minterms 1,3,7 with 2 and 6 to simplify to \( B \times C \).
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Which of the following is NOT a valid Boolean law or theorem?
C · Identity Law: \( A + 1 = 0 \)
Identity Law states \( A + 1 = 1 \), not 0. Option C is incorrect.
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Simplify the Boolean expression \( \overline{(A + B)} + AB \).
A · 1
Using consensus theorem and complementarity, the expression simplifies to 1.
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Refer to the Karnaugh map below. What is the simplified expression for the logic function?

AB C 1 1 1 0 0 1
A · \( A + \overline{B}C \)
Grouping the 1s in the K-map leads to the simplified expression \( A + \overline{B}C \).

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