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GATE 2024 PH – Question 32

Electronics · basics of digital logic circuits, combinational and sequential circuits, flip- flops, timers, counters, registers, A/D and D/A conversion. · 1 mark · Numerical answer

The minimum number of basic logic gates to realize $B\cdot(A+B)+A\cdot(\bar B+A)$ is _____ (in integer).

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Correct answer: 1

Explanation

Simplify the expression using Boolean algebra:
$$B\cdot(A+B)+A\cdot(\bar B+A).$$

**First term (absorption law):** $B(A+B)=BA+B=B(A+1)=B$.

**Second term:** $A(\bar B+A)=A\bar B+A=A(\bar B+1)=A$.

**Sum:**
$$B+A=A+B .$$

The expression is just $A+B$, which needs **one OR gate**. The minimum number of basic gates is **1**.