Aspire Faculty ID #12042 · Topic: NIMCET 2025 · Just now
NIMCET 2025

Consider the Boolean function in a CPU control unit: \[ Y = (A + B\cdot \overline{C}) \cdot (\overline{A}\cdot B + C) \]

Solution

Given: $Y = (A + B\overline{C}).(\overline{A}B + C)$ 
Single-Step Smart Trick (Pair Matching Rule): 
Multiply only the terms that can logically combine: 
$A$ pairs only with $C$ → gives $AC$ 
 $B\overline{C}$ pairs only with $\overline{A}B$ → gives $\overline{A}B\overline{C}$ 
 So directly: $Y = AC + \overline{A}B\overline{C}$
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