From the logic gate diagram given below, derive the Boolean expression for (1), (2) and Q. Reduce…
From the logic gate diagram given below, derive the Boolean expression for (1), (2) and Q. Reduce the derived expression.
Answer
Answer
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From the given logic gate diagram:
1. Expression for (1):
The top gate is a 3-input AND gate with inputs A, B, and C.
(1) = A • B • C
2. Expression for (2):
Input A passes through to a 2-input AND gate.
Inputs B and C pass through NOT gates to produce B' and C', which enter a 2-input OR gate to produce (B' + C').
The 2-input AND gate takes inputs A and (B' + C').
(2) = A • (B' + C')
3. Expression for Q:
Outputs (1) and (2) enter a 2-input OR gate.
Q = (1) + (2) = A • B • C + A • (B' + C')
4. Reduction of Q:
Q = A • [B • C + (B' + C')]
By De Morgan's Law: B' + C' = (B • C)'
Q = A • [B • C + (B • C)']
By Complement Law: X + X' = 1 (where X = B • C)
Q = A • 1
By Identity Law: Q = A
Reduced expression: Q = A
From ISC 2026 Computer Science Paper 1, question 5(ii).