Number System and Boolean Algebra for GATE – Complete Notes with PYQ

Digital Logic - Number System (Top 10 GATE Questions)

Ye 10 questions GATE ECE / CSE me baar-baar puche gaye hain. Har question ke neeche solution hai.

Q1. Convert (1011.01)₂ to Decimal.

A) 11.25 B) 11.5 C) 10.25 D) 10.5

View Solution

(1011)₂ = 8+2+1 = 11
(.01)₂ = 0.25
Answer = 11.25 (Option A)

Q2. Hexadecimal (2F)₁₆ to Decimal?

A) 45 B) 46 C) 47 D) 48

View Solution

2×16¹ + 15×16⁰ = 32 + 15 = 47
Answer = 47 (Option C)

Q3. Simplify: F = A + A'B

A) A B) A+B C) B D) AB

View Solution

A + A'B = (A+A')(A+B) = 1.(A+B) = A+B
Answer = A+B (Option B)

Q4. 2's complement of (1010)₂ is?

A) 0110 B) 0101 C) 0110 D) 1010

View Solution

1's complement = 0101, +1 = 0110
Answer = 0110 (Option A/C)

Q5. (1101)₂ XOR (1011)₂ = ?

A) 0110 B) 1111 C) 1001 D) 0111

View Solution

1 xor 1=0, 1 xor 0=1...
1101 xor 1011 = 0110
Answer = 0110 (Option A)

Q6. Simplify: AB + AB' = ?

A) A B) B C) A+B D) 0

View Solution

AB + AB' = A(B+B') = A.1 = A
Answer = A (Option A)

Q7. Decimal 25 to Binary?

A) 11001 B) 11000 C) 10011 D) 11011

View Solution

25 = 16+8+1 = 11001
Answer = 11001 (Option A)

Q8. De Morgan: (A+B)' = ?

A) A'B' B) A'+B' C) AB D) A'B

View Solution

De Morgan Law se (A+B)' = A' . B'
Answer = A'B' (Option A)

Q9. (101)₂ × (11)₂ = ?

A) 1111 B) 1011 C) 1110 D) 1010

View Solution

5 × 3 = 15 = (1111)₂
Answer = 1111 (Option A)

Q10. Octal (72)₈ = Binary?

A) 111010 B) 101010 C) 111000 D) 110010

View Solution

7=111, 2=010 => 111010
Answer = 111010 (Option A)

✅ Next: Combinational Circuits (MUX, Decoder) ke 10 Questions chahiye kya Bhai?