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Verify the following expression by using the truth table:
Verify the following expression by using the truth table:
$(A \odot B)' = (A \oplus B)$
Answer
Answer
AI$A \odot B$ (XNOR) $= A'B' + AB$ and $A \oplus B$ (XOR) $= A'B + AB'$.
The columns $(A \odot B)'$ and $A \oplus B$ are identical for all inputs, hence $(A \odot B)' = A \oplus B$. Verified.
| A | B | $A \odot B$ | $(A \odot B)'$ | $A \oplus B$ |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 |
From ISC 2023 Computer Science Paper 1, question 4(iii).