Q1. The binary equivalent of decimal number 45 is:
A) 101100
B) 101101
C) 110101
D) 101110
✅ Answer: B) 101101
💡 Explanation: 45 = 32+8+4+1 = 2^5+2^3+2^2+2^0 = 101101 in binary.
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Q2. The decimal equivalent of binary number 1101101 is:
A) 101
B) 109
C) 105
D) 107
✅ Answer: B) 109
💡 Explanation: 1101101 = 64+32+8+4+1 = 109 in decimal.
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Q3. Hexadecimal number 2F in decimal is:
A) 45
B) 47
C) 63
D) 37
✅ Answer: B) 47
💡 Explanation: 2F hex = (2×16) + (15×1) = 32 + 15 = 47 in decimal.
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Q4. The 1’s complement of binary number 10110101 is:
A) 01001011
B) 01001010
C) 10110100
D) 11001010
✅ Answer: A) 01001011
💡 Explanation: 1’s complement inverts every bit: 10110101 → 01001010.
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Q5. The octal equivalent of binary 111010110 is:
A) 726
B) 356
C) 726
D) 7261
✅ Answer: A) 726
💡 Explanation: Group from right in 3s: 111|010|110 = 7|2|6 = 726 in octal.
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Q6. In Boolean algebra, A + A’ equals:
A) 0
B) A
C) 1
D) A’
✅ Answer: C) 1
💡 Explanation: A + A’ = 1 (Complement Law). A variable OR its complement always equals 1.
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Q7. The hexadecimal equivalent of decimal 255 is:
A) EF
B) FE
C) FF
D) EE
✅ Answer: C) FF
💡 Explanation: 255 = (15×16) + 15 = FF in hexadecimal. Both digits are F (=15 in decimal).
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Q8. 2’s complement representation is used in computers to represent:
A) Floating point numbers only
B) Negative integers
C) Hexadecimal numbers
D) Octal numbers
✅ Answer: B) Negative integers
💡 Explanation: 2’s complement is the standard method used by computers to represent negative integers in binary.
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Q9. What is the result of XOR operation: 1010 XOR 1100?
A) 1110
B) 0110
C) 0111
D) 1010
✅ Answer: B) 0110
💡 Explanation: XOR: 1⊕1=0, 0⊕1=1, 1⊕0=1, 0⊕0=0. 1010 XOR 1100 = 0110.
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Q10. In Boolean algebra, De Morgan’s theorem states:
A) (A+B)’ = A’.B’ and (A.B)’ = A’+B’
B) (A+B)’ = A+B and (A.B)’ = A.B
C) A’ = A and B’ = B
D) A+B = A.B
✅ Answer: A) (A+B)’ = A’.B’ and (A.B)’ = A’+B’
💡 Explanation: De Morgan’s theorem: NOT(A OR B) = (NOT A) AND (NOT B), and NOT(A AND B) = (NOT A) OR (NOT B).
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Q11. The binary addition 1011 + 1101 equals:
A) 11000
B) 11001
C) 10111
D) 11010
✅ Answer: A) 11000
💡 Explanation: 1011 + 1101: 1+1=10, carry 1; 1+0+1=10, carry 1; 0+1+1=10, carry 1; 1+1+1=11. Result = 11000.
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Q12. How many bits are required to represent the decimal number 200 in binary?
A) 6 bits
B) 7 bits
C) 8 bits
D) 9 bits
✅ Answer: C) 8 bits
💡 Explanation: 200 in binary = 11001000. It requires 8 bits. (2^7=128, 2^8=256, so 8 bits needed for 200).
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Q13. The NAND gate is called ‘universal gate’ because:
A) It is used in all computers
B) Any Boolean function can be implemented using only NAND gates
C) It is the fastest logic gate
D) It consumes the least power
✅ Answer: B) Any Boolean function can be implemented using only NAND gates
💡 Explanation: NAND (and NOR) are universal gates — all other logic gates (AND, OR, NOT, XOR) can be constructed from them.
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Q14. The Gray code for decimal 5 is:
A) 0101
B) 0100
C) 0111
D) 0110
✅ Answer: C) 0111
💡 Explanation: Decimal 5 = binary 0101. Gray code: MSB same (0), then XOR consecutive bits: 0, 0⊕1=1, 1⊕0=1, 0⊕1=1 → 0111.
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Q15. Octal number 17 in decimal is:
A) 13
B) 15
C) 17
D) 8
✅ Answer: B) 15
💡 Explanation: Octal 17 = (1×8) + (7×1) = 8 + 7 = 15 in decimal.
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Q16. In a half adder, which gates are used?
A) OR and NOT gates
B) XOR and AND gates
C) NAND and NOR gates
D) AND and OR gates
✅ Answer: B) XOR and AND gates
💡 Explanation: A half adder uses an XOR gate (for sum) and an AND gate (for carry). It adds two single bits.
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Q17. The 2’s complement of binary number 00110100 is:
A) 11001011
B) 11001100
C) 11001101
D) 01001100
✅ Answer: B) 11001100
💡 Explanation: Step 1 – 1’s complement of 00110100 = 11001011. Step 2 – Add 1: 11001011 + 1 = 11001100.
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Q18. Boolean expression A.(A+B) simplifies to:
A) A+B
B) A.B
C) A
D) B
✅ Answer: C) A
💡 Explanation: Absorption Law: A.(A+B) = A. This is because A.A + A.B = A + A.B = A (since A absorbs A.B).
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Q19. The base of the hexadecimal number system is:
A) 2
B) 8
C) 10
D) 16
✅ Answer: D) 16
💡 Explanation: Hexadecimal is base-16, using digits 0–9 and letters A–F (where A=10, B=11, C=12, D=13, E=14, F=15).
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Q20. BCD (Binary Coded Decimal) represents each decimal digit using:
A) 2 bits
B) 4 bits
C) 8 bits
D) 16 bits
✅ Answer: B) 4 bits
💡 Explanation: BCD encodes each decimal digit (0–9) as a 4-bit binary group. For example, 9 = 1001 in BCD.