Project ForgeConsider three 4-variable functions f1, f2, and f3, expressed in sum-of-minterms as f1=Σ(0,2,5,8,14), f2=Σ(2,3,6,8,14,15), f3=Σ(2,7,11,14). For a circuit with one AND gate (computing f1 AND f2) feeding one XOR gate together with f3 (computing (f1·f2)⊕f3), the output function f can be expressed as:
- Σ(7,8,11)
- BΣ(2,7,8,11,14)
- CΣ(2,14)
- DΣ(0,2,3,5,6,7,8,11,14,15)
Explanation
f1∧f2 = intersection of minterm sets {0,2,5,8,14}∩{2,3,6,8,14,15} = {2,8,14}. f = (f1∧f2) ⊕ f3 = symmetric difference of {2,8,14} and {2,7,11,14} — minterms in exactly one set: {8} (only in f1∧f2) and {7,11} (only in f3); 2 and 14 appear in BOTH so they cancel under XOR. Result: Σ(7,8,11).
Source: GATE CS 2019 (Set-2) (2019)
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