📘 DIGITAL NUMBER SYSTEM & LOGIC GATES for crpf radio operator, cipher and radio fitter

🔥 MASTER PRACTICE SET – 50 MCQs

(One-Stop Complete Preparation)

🔢 SECTION A: NUMBER SYSTEM – COMPLETE CONVERSIONS (25 MCQs)

Q1. Convert the binary number

(101101)2(101101)_2(101101)2​

into decimal.

A. 43
B. 44
C. 45
D. 46

Answer: C

Explanation: 1⋅25+0⋅24+1⋅23+1⋅22+0⋅21+1⋅20=32+8+4+1=451·2^5 + 0·2^4 + 1·2^3 + 1·2^2 + 0·2^1 + 1·2^0 = 32 + 8 + 4 + 1 = 451⋅25+0⋅24+1⋅23+1⋅22+0⋅21+1⋅20=32+8+4+1=45

Q2. Convert the octal number

(745)8(745)_8(745)8​

into decimal.

A. 485
B. 489
C. 493
D. 501

Answer: B

Explanation: 7⋅82+4⋅81+5⋅80=448+32+5=4897·8^2 + 4·8^1 + 5·8^0 = 448 + 32 + 5 = 4897⋅82+4⋅81+5⋅80=448+32+5=489

Q3. Convert the hexadecimal number

(9C)16(9C)_{16}(9C)16​

into decimal.

A. 154
B. 156
C. 158
D. 160

Answer: B

Explanation:
C = 12 9⋅16+12=1569·16 + 12 = 1569⋅16+12=156

Q4. Convert the decimal number

(512)10(512)_{10}(512)10​

into binary.

A. 100000000
B. 1000000000
C. 111111111
D. 110000000

Answer: B

Explanation: 512=29⇒1 followed by 9 zeros512 = 2^9 \Rightarrow 1\text{ followed by 9 zeros}512=29⇒1 followed by 9 zeros

Q5. Convert the binary number

(1101101)2(1101101)_2(1101101)2​

into octal.

A. 155
B. 165
C. 175
D. 145

Answer: A

Explanation: 001  101  101⇒1  5  5001\;101\;101 \Rightarrow 1\;5\;5001101101⇒155

Q6. Convert the binary number

(10101111)2(10101111)_2(10101111)2​

into hexadecimal.

A. AF
B. BF
C. 9F
D. CF

Answer: A

Explanation: 1010=A,  1111=F1010 = A,\;1111 = F1010=A,1111=F

Q7. Convert the hexadecimal number

(3A)16(3A)_{16}(3A)16​

into binary.

A. 00111010
B. 00110110
C. 00111100
D. 00101010

Answer: A

Explanation:
3 → 0011
A → 1010

Q8. Convert the octal number

(57)8(57)_8(57)8​

into binary.

A. 101111
B. 110101
C. 111001
D. 101011

Answer: A

Explanation:
5 → 101
7 → 111

Q9. Convert the binary fraction

(0.101)2(0.101)_2(0.101)2​

into decimal.

A. 0.5
B. 0.625
C. 0.75
D. 0.875

Answer: B

Explanation: 1⋅2−1+0⋅2−2+1⋅2−3=0.5+0+0.125=0.6251·2^{-1} + 0·2^{-2} + 1·2^{-3} = 0.5 + 0 + 0.125 = 0.6251⋅2−1+0⋅2−2+1⋅2−3=0.5+0+0.125=0.625

Q10. Convert the decimal fraction

(0.625)10(0.625)_{10}(0.625)10​

into binary.

A. 0.101
B. 0.110
C. 0.111
D. 0.100

Answer: A

Explanation:
Repeated multiplication by 2 gives 0.101₂

Q11. How many bits are required to represent

(FFFF)_{16} \] ? A. 8 B. 12 C. 16 D. 20 **Answer:** C **Explanation:** 1 hex digit = 4 bits \[ 4×4 = 16

Q12. The decimal equivalent of

(11111111)2(11111111)_2(11111111)2​

is:

A. 254
B. 255
C. 256
D. 257

Answer: B

Explanation: 28−1=2552^8 – 1 = 25528−1=255

Q13. Convert

(100100)2(100100)_2(100100)2​

into decimal.

A. 34
B. 36
C. 38
D. 40

Answer: B

Q14. Convert

(64)10(64)_{10}(64)10​

into octal.

A. 80
B. 90
C. 100
D. 110

Answer: C

Q15. One octal digit is equivalent to how many binary bits?

A. 2
B. 3
C. 4
D. 8

Answer: B

Q16. Convert

(1A3)16(1A3)_{16}(1A3)16​

into decimal.

A. 418
B. 419
C. 420
D. 421

Answer: C

Q17. Which conversion uses repeated division method?

A. Binary → Decimal
B. Decimal → Binary
C. Binary → Hexadecimal
D. Octal → Binary

Answer: B

Q18. The MSB of a binary number has:

A. Least weight
B. Zero weight
C. Highest weight
D. Constant value

Answer: C

Q19. Convert

(256)10(256)_{10}(256)10​

into hexadecimal.

A. 80
B. 100
C. FF
D. 110

Answer: B

Q20. Convert the binary number

(111000)2(111000)_2(111000)2​

into octal.

A. 70
B. 72
C. 74
D. 76

Answer: C

Q21. Convert the decimal number

(1024)10(1024)_{10}(1024)10​

into binary.

A. 1000000000
B. 10000000000
C. 1111111111
D. 11000000000

Answer: B

Q22. Convert the binary fraction

(0.11)2(0.11)_2(0.11)2​

into decimal.

A. 0.5
B. 0.75
C. 0.625
D. 0.875

Answer: B

Q23. Convert the octal number

(377)8(377)_8(377)8​

into decimal.

A. 247
B. 255
C. 263
D. 271

Answer: B

Q24. Convert

(FF)16(FF)_{16}(FF)16​

into decimal.

A. 254
B. 255
C. 256
D. 257

Answer: B

Q25. Binary subtraction is performed in base:

A. 10
B. 8
C. 2
D. 16

Answer: C

⚙️ SECTION B: LOGIC GATES – TRUTH TABLE + EQUATION (25 MCQs)

Q26. Identify the gate represented by

Y=AB‾+A‾BY = A\overline{B} + \overline{A}BY=AB+AB

A. AND
B. OR
C. XOR
D. XNOR

Answer: C

Explanation:
This is the standard Boolean equation of XOR gate.

Q27. Identify the gate represented by

Y=(A+B)′Y = (A + B)’Y=(A+B)′

A. NAND
B. NOR
C. AND
D. XOR

Answer: B

Q28. Identify the gate represented by

Y=(A⋅B)′Y = (A·B)’Y=(A⋅B)′

A. AND
B. OR
C. NAND
D. NOR

Answer: C

Q29. For a 2-input AND gate, output = 1 occurs how many times?

A. 0
B. 1
C. 2
D. 3

Answer: B

Q30. For which input does a NOR gate give output 1?

A. 00
B. 01
C. 10
D. 11

Answer: A

Q31. Simplify:

Y=A+A⋅BY = A + A·BY=A+A⋅B

A. AB
B. A
C. A + B
D. B

Answer: B

Q32. Simplify:

Y=A⋅A′Y = A·A’Y=A⋅A′

A. 1
B. A
C. A’
D. 0

Answer: D

Q33. According to De Morgan’s theorem:

(A+B)′=(A + B)’ =(A+B)′=

A. A’ + B’
B. A’B’
C. AB
D. (AB)’

Answer: B

Q34. Output of XOR gate is 1 when:

A. Inputs are same
B. Inputs are different
C. All inputs are 1
D. All inputs are 0

Answer: B

Q35. XNOR gate is also called:

A. Difference detector
B. Equality detector
C. Inverter
D. Buffer

Answer: B

Q36. NAND gate is an inverted form of:

A. OR
B. AND
C. XOR
D. NOR

Answer: B

Q37. NOR gate is an inverted form of:

A. AND
B. OR
C. XOR
D. NAND

Answer: B

Q38. Which gate behaves as NOT gate when inputs are shorted?

A. AND
B. OR
C. NAND
D. XOR

Answer: C

Q39. Number of input combinations in a 3-input gate is:

A. 6
B. 8
C. 10
D. 16

Answer: B

Q40. Half adder SUM output is obtained using:

A. AND
B. OR
C. XOR
D. NAND

Answer: C

Q41. Half adder CARRY output is obtained using:

A. AND
B. OR
C. XOR
D. NOR

Answer: A

Q42. Full adder has how many inputs?

A. 2
B. 3
C. 4
D. 5

Answer: B

Q43. Output of

(A⊕B)′(A ⊕ B)'(A⊕B)′

is equivalent to which gate?

A. XOR
B. XNOR
C. NAND
D. NOR

Answer: B

Q44. Truth table of which gate has output = 1 exactly twice?

A. AND
B. OR
C. XOR
D. NOR

Answer: C

Q45. Buffer gate is used for:

A. Inversion
B. Isolation
C. Addition
D. Comparison

Answer: B

Q46. Universal gates are:

A. AND, OR
B. OR, NOT
C. NAND, NOR
D. XOR, XNOR

Answer: C

Q47. Output of NOR gate for inputs (1,1) is:

A. 0
B. 1
C. Undefined
D. High

Answer: A

Q48. Which gate is used in parity checking?

A. AND
B. OR
C. XOR
D. NAND

Answer: C

Q49. Boolean algebra was introduced by:

A. Newton
B. Shannon
C. Boole
D. Maxwell

Answer: C

Q50. Logic gates are the basic building blocks of:

A. Analog systems
B. Mechanical systems
C. Digital systems
D. Optical systems

Answer: C