Find the Boolean Expression F which is represented in the following Truth…
2026
Find the Boolean Expression F which is represented in the following Truth Table:
A | B | F |
|---|---|---|
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
- A.
A'·B + A·B'
- B.
A' + A·B'
- C.
A'·B + B'
- D.
A·B + A'·B'
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Correct answer: A
CONCEPT: The Sum-of-Products (SOP) canonical form expresses a Boolean function directly from its truth table: for every input combination where the output is 1, write the corresponding minterm (each variable appears uncomplemented if it is 1 in that row, complemented if it is 0), then OR (sum) all such minterms together.
APPLICATION -- applying this to the given truth table:
Row A=0, B=0 gives F=0, so this row contributes no term.
Row A=0, B=1 gives F=1, so this row contributes the minterm A'B.
Row A=1, B=0 gives F=1, so this row contributes the minterm AB'.
Row A=1, B=1 gives F=0, so this row contributes no term.
Summing the two contributing minterms gives F = A'B + AB'.
CROSS-CHECK: this expression is 1 exactly when A and B differ (Exclusive-OR behaviour) and 0 when they match, which is exactly the pattern in the truth table -- confirming the derivation.