Project ForgeGiven f1, f3 and f in canonical sum of products form (in decimal) for the circuit where f1 and f2 feed an AND gate, whose output ORs with f3 to produce f: f1 = Σm(4,5,6,7,8), f3 = Σm(1,6,15), f = Σm(1,6,8,15). Then f2 is
- AΣm(4,6)
- BΣm(4,8)
- Σm(6,8)
- DΣm(4,6,8)
Explanation
f = f1·f2 + f3. Since f1·f2's value only matters at positions where f1=1 (i.e. {4,5,6,7,8}), f2 must be 0 at any of these positions NOT in f (4,5,7 — since f lacks them), else f would wrongly include them. f2 must be 1 at 8 (needed, since f has minterm 8 which isn't in f3). Position 6 is free (already covered by f3, so f1f2 including it is harmless). Testing f2=Σm(6,8): f1·f2={6,8}, plus f3={1,6,15} gives {1,6,8,15} — matches f exactly. Options with 4 (A,B,D) are invalid since they'd wrongly add minterm 4 to f.
Source: GATE CS 2008 (2008)
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