UGC NET Paper 1 — ICT
20 MCQs: Number System Conversions
Binary → Decimal
1. What is the decimal equivalent of (1010)₂?
A) 8
B) 10
C) 12
D) 14
Answer: B) 10
Explanation:
1010₂ = (1×2³) + (0×2²) + (1×2¹) + (0×2⁰)
= 8 + 0 + 2 + 0 = 10
2. Convert (1101)₂ into decimal.
A) 11
B) 12
C) 13
D) 14
Answer: C) 13
Explanation: 8 + 4 + 0 + 1 = 13
3. What is (101101)₂ in decimal?
A) 43
B) 44
C) 45
D) 46
Answer: C) 45
Explanation: 32 + 8 + 4 + 1 = 45
4. Convert (11111111)₂ to decimal.
A) 127
B) 255
C) 256
D) 128
Answer: B) 255
Explanation: 128+64+32+16+8+4+2+1 = 255
5. The decimal equivalent of (100101)₂ is:
A) 35
B) 36
C) 37
D) 38
Answer: C) 37
Explanation: 32 + 4 + 1 = 37
Decimal → Binary
6. Convert (10)₁₀ into binary.
A) 1000
B) 1010
C) 1100
D) 1110
Answer: B) 1010₂
Explanation: 10 = 8 + 2 = 2³ + 2¹
7. What is the binary equivalent of decimal 25?
A) 11001
B) 10101
C) 11100
D) 10011
Answer: A) 11001₂
Explanation: 25 = 16 + 8 + 1
8. Convert decimal 42 into binary.
A) 101010
B) 101100
C) 110010
D) 100110
Answer: A) 101010₂
Explanation: 42 = 32 + 8 + 2
9. The binary representation of decimal 64 is:
A) 100000
B) 1000000
C) 1100000
D) 1111111
Answer: B) 1000000₂
Explanation: 64 = 2⁶, so it is 1 followed by six zeros.
10. Convert decimal 75 into binary.
A) 1001011
B) 1010011
C) 1001101
D) 1101001
Answer: A) 1001011₂
Explanation: 75 = 64 + 8 + 2 + 1
Binary → Octal
11. Convert (101)₂ into octal.
A) 4
B) 5
C) 6
D) 7
Answer: B) 5
Explanation: Group binary digits in sets of 3: 101₂ = 5₈.
12. What is the octal equivalent of (110101)₂?
A) 64
B) 65
C) 66
D) 67
Answer: B) 65₈
Explanation:
110 101 → 6 5
Therefore, (110101)₂ = (65)₈.
13. Convert (111011)₂ into octal.
A) 71
B) 72
C) 73
D) 74
Answer: C) 73₈
Explanation: 111 011 → 7 3.
14. What is (1011011)₂ in octal?
A) 123
B) 133
C) 113
D) 143
Answer: A) 133₈
Explanation: Add leading zero: 001 011 011 → 1 3 3.
15. Convert (11111111)₂ into octal.
A) 377
B) 357
C) 367
D) 377
Answer: A) 377₈
Explanation: 011 111 111 → 3 7 7.
Octal → Binary
16. Convert (5)₈ into binary.
A) 100
B) 101
C) 110
D) 111
Answer: B) 101₂
Explanation: Each octal digit corresponds to 3 binary bits: 5 → 101.
17. What is the binary equivalent of (27)₈?
A) 10111
B) 11011
C) 11101
D) 10011
Answer: B) 10111₂
Correction: 2 → 010 and 7 → 111, giving 010111₂ = 10111₂.
So the correct answer is A) 10111.
18. Convert (45)₈ into binary.
A) 100101
B) 101001
C) 100111
D) 110101
Answer: A) 100101₂
Explanation: 4 → 100, 5 → 101 → 100101.
19. What is the binary equivalent of (126)₈?
A) 1010110
B) 1010010
C) 1100110
D) 1110110
Answer: A) 1010110₂
Explanation: 1 → 001, 2 → 010, 6 → 110 → 001010110, removing leading zeros gives 1010110.
20. Convert (753)₈ into binary.
A) 111101011
B) 111110011
C) 101101011
D) 110101111
Answer: A) 111101011₂
Explanation:
7 → 111
5 → 101
3 → 011
Therefore: 111 101 011 = 111101011₂.
Quick Trick to Remember
Binary ↔ Octal: Group binary digits in 3s.
| Octal | Binary |
|---|---|
| 0 | 000 |
| 1 | 001 |
| 2 | 010 |
| 3 | 011 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
Binary → Decimal: Multiply each bit by its corresponding power of 2 and add.
Decimal → Binary: Repeatedly divide by 2 and read the remainders from bottom to top.
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