Project ForgeDigital Logic
Boolean Algebra & Minimization
GATE 2020
Medium
Consider the Boolean function z(a,b,c), realized by a circuit where z = a OR (NOT(b) AND c) [i.e. a NOT gate inverts b, an AND gate combines NOT(b) with c, and an OR gate combines a with that AND output to produce z]. Which one of the following minterm lists represents the circuit given above?
- AΣ(0,1,3,7)
- Σ(1,4,5,6,7)
- CΣ(2,4,5,6,7)
- DΣ(2,3,5)
Explanation
z = a + b'c. Evaluate z for all 8 combinations of (a,b,c) read as minterm index abc: 000→0+1·0=0; 001→0+1·1=1 (m1); 010→0+0·0=0; 011→0+0·1=0; 100→1 (m4); 101→1 (m5); 110→1 (m6); 111→1 (m7). So z = Σ(1,4,5,6,7).
Source: GATE CS 2020 (2020)
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