Question 1 of 5
Why is the binary number system widely used in computer systems?
A
It is easy for humans to understand
B
It uses only two digits, 0 and 1, which can be easily represented by electronic switches
C
It allows for more precise calculations
D
It is the most efficient for mental arithmetic
Why: Computers use electronic circuits that have two stable states: on (1) and off (0). The binary system, using only digits 0 and 1, perfectly matches this hardware capability, making it simple and reliable for digital logic operations, storage, and processing. This design minimizes errors and complexity in circuit design. Option B correctly identifies this fundamental reason.
Question 2 of 5
Convert the hexadecimal number 25 to binary.
Why: To convert hexadecimal 25 to binary, convert each hex digit separately. Hex digit 2 is \( 0010_2 \) (since 2 = 2^1). Hex digit 5 is \( 0101_2 \) (5 = 4+1 = 2^2 + 2^0). Combining gives 0010 0101, or 00100101 in 8-bit form. Verification: Binary 00100101 = 32+4+1 = 37 decimal, and hex 25 = 2*16 + 5 = 37 decimal, which matches.
Question 3 of 5
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
B
1011 + 1101 = 10000
C
1011 + 1101 = 1110
D
1011 + 1101 = 10010
Why: Perform binary addition step by step:
1011
+1101
-----
Start from right: 1+1=10 (write 0, carry 1); 1+0+1(carry)=10 (0, carry 1); 0+1+1(carry)=10 (0, carry 1); 1+1+1(carry)=11 (1, carry 1); carry 1 makes 11000. Decimal check: 11 + 13 = 24, binary 11000=24. Option A is correct.
Question 4 of 5
What is the result of binary multiplication 101 × 11?
Why: Binary multiplication 101 × 11:
101
× 11
----
101 (101 × 1, shifted 0)
101 (101 × 1, shifted 1)
-----
1111 (add: 101 + 1010 = 1111).
Decimal verification: 5 × 3 = 15, binary 1111=15. Step-by-step: First partial 101 (shift 0), second 101 shifted left by 1 becomes 1010, sum 101 + 1010: right column 1+0=1, 0+1=1, 1+0+1(carry? wait: positions: 0101 + 1010 = from right:1+0=1, 0+1=1, 1+0=1, 0+1=1 → 1111).
Question 5 of 5
Convert the binary number 101101 to its decimal equivalent.
Why: Binary 101101 to decimal: Positions from right (starting at 2^0): 1*2^0=1, 0*2^1=0, 1*2^2=4, 1*2^3=8, 0*2^4=0, 1*2^5=32. Sum: 32+8+4+1=45. Formula: \( 1\times2^5 + 0\times2^4 + 1\times2^3 + 1\times2^2 + 0\times2^1 + 1\times2^0 = 32 + 0 + 8 + 4 + 0 + 1 = 45 \).
