26. To convert binary to hexadecimal, bits are grouped in sets of:
- 3
- 4
- 2
- 16
Answer: B) 4
Explanation: 16 = 2⁴.
MCQs / Computer Science / Number Systems and Conversions
Number Systems and Conversions MCQs — Computer Science (page 2)
55 multiple-choice questions on Number Systems and Conversions from Computer Science, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.
27. The place value of the third digit from the right in a binary number is:
- 4
- 8
- 3
- 2
Answer: A) 4
Explanation: Positions 0,1,2 → 2⁰=1, 2¹=2, 2²=4.
28. Which of the following is NOT a valid binary number?
- 1011
- 1111
- 1000
- 1021
Answer: D) 1021
Explanation: Binary allows only 0 and 1.
29. To convert binary to octal, bits are grouped in sets of:
- 8
- 3
- 4
- 2
Answer: B) 3
Explanation: 8 = 2³.
30. (100)₁₆ in decimal is:
- 64
- 100
- 256
- 160
Answer: C) 256
Explanation: 1×16² = 256.
31. (1111)₂ in decimal is:
- 14
- 16
- 31
- 15
Answer: D) 15
Explanation: 8 + 4 + 2 + 1 = 15.
32. The 1's complement of 1010 is:
- 1011
- 1010
- 0101
- 0110
Answer: C) 0101
Explanation: Flip every bit.
33. When converting decimal to binary by repeated division, the remainders are read:
- from bottom to top
- from top to bottom
- only the first remainder
- in any order
Answer: A) from bottom to top
Explanation: The last remainder is the MSB.
34. (100)₁₀ in octal is:
- 100
- 164
- 124
- 144
Answer: D) 144
Explanation: 1×64 + 4×8 + 4 = 100.
35. (3AF)₁₆ in binary is:
- 1110111010
- 1110101111
- 1111010101
- 1010111111
Answer: B) 1110101111
Explanation: 0011 1010 1111.
36. (101101)₂ in decimal is:
- 46
- 45
- 54
- 37
Answer: B) 45
Explanation: 32 + 8 + 4 + 1 = 45.
37. Computers use the binary system because:
- electronic circuits have two stable states (on/off)
- it has ten digits
- binary numbers are shorter than decimal
- humans prefer binary
Answer: A) electronic circuits have two stable states (on/off)
Explanation: Two states map naturally to 0 and 1.
38. (A5)₁₆ in decimal is:
- 105
- 165
- 175
- 155
Answer: B) 165
Explanation: 10×16 + 5 = 165.
39. In hexadecimal, C represents:
- 12
- 11
- 14
- 13
Answer: A) 12
Explanation: A=10, B=11, C=12.
40. (17)₈ in decimal is:
- 17
- 23
- 15
- 7
Answer: C) 15
Explanation: 1×8 + 7 = 15.
41. (1011)₂ + (0110)₂ equals:
- 11001
- 10101
- 1111
- 10001
Answer: D) 10001
Explanation: 11 + 6 = 17 = 10001.
42. (725)₈ in hexadecimal is:
- 1E5
- 5D1
- 2D5
- 1D5
Answer: D) 1D5
Explanation: 111 010 101 → 0001 1101 0101.
43. (1011011101)₂ in hexadecimal is:
- 2DD
- 2ED
- B71
- 5BA
Answer: A) 2DD
Explanation: 0010 1101 1101 → 2 D D.
44. In binary subtraction, 0 − 1 requires:
- division by 2
- a carry to the next bit
- a borrow from the next higher bit
- no action
Answer: C) a borrow from the next higher bit
Explanation: Like decimal borrowing.
45. (B6)₁₆ in octal is:
- 662
- 266
- 256
- 276
Answer: B) 266
Explanation: 1011 0110 → 010 110 110 → 2 6 6.
46. (11111111)₂ in hexadecimal is:
- FF
- 377
- 77
- EE
Answer: A) FF
Explanation: 1111 1111 → F F.
47. The easiest way to convert octal to hexadecimal is:
- directly digit by digit
- through binary
- by adding 8
- by multiplying by 2
Answer: B) through binary
Explanation: Octal → binary (3 bits) → regroup in 4s → hex.
48. The 2's complement of 1010 is:
- 0110
- 0101
- 1011
- 0111
Answer: A) 0110
Explanation: 0101 + 1 = 0110.
49. (377)₈ in hexadecimal is:
- 377
- 1FF
- 7F
- FF
Answer: D) FF
Explanation: (377)₈ = 255 = FF.
50. In binary, 1 + 1 + 1 equals:
- 3
- 111
- 10
- 11
Answer: D) 11
Explanation: Write 1, carry 1.
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