The given circuit translates to which equation?

Question

BlackTom AI · Accepted Answer

We are given a circuit and four candidate Boolean expressions to match. I'll evaluate each option in turn and relate it to the Karnaugh-map-looking diagram provided.

Option 1: y = a’ + b’ + c
This expression would produce a true output whenever a is 0, or b is 0, or c is 1. In terms of the map, that would turn on many cells beyond the ones shown in the diagram (it would cover all minterms with a=0, plus additional minterms when c=1 regardless of a and b). Since the diagram does not indicate such widespread coverage, this option is unlikely to be correct.

Option 2: y = a’b’ + c
Here, the term a’b’ activates when a=0 and b=0 (for all c), and the term c activates when c=1 (for all a and b). This combination would produce a different set of true cases than shown in the map, particularly it would force the output high for some cells with a=0 and b≠0 and/or c=0 that the diagram does not indicate. Thus this is not a match.

Option 3: y = a’ + b’c
This expression says: output is 1 if a=0 (the a’ term covers all cells with a=0), or if b=0 and c=1 (the b’c term covers the remaining necessary case when a=1). In a typical K-map simplification, grouping all cells with a=0 yields the a’ term, and then a single additional implicant b’c accounts for the remaining 1s that aren’t covered by a’ alone. This combination aligns with the common minimal form derived from a map where the ones are distributed across a=0 and the (a=1, b=0, c=1) cell.

Option 4: y = a’ + bc
This would activate for a=0 (a’ term) or when b=1 and c=1 (bc term). The bc term would set many cells to 1 when b and c are both 1, including some cells not indicated as 1 in the diagram. That would again not match the given map, so this option is not correct.

In summary, the only option that matches the diagram’s pattern—covering all a=0 cells plus the specific a=1, b=0, c=1 case with an additional implicant—is y = a’ + b’c. The other expressions either overcover the map or miss the required 1s in certain cells, making them incorrect.

S2501-CPSC-3300-001-11767 Exam 1

The given circuit translates to which equation?

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