Question
Download Solution PDFThe expression \(\overline{A\oplus B}\) is equal to _____.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct option is option 2.
Concept:
De Morgan's law equations are :
(P.Q)' → P' + Q'
(P+Q)' → P' . Q'
Explanation:
( A ⊕ B )' = ( A'B + AB' )'
= ( A'B )' . ( AB' )' [By using De Morgan's Law]
= ( A'' + B' ) . ( A' + B'' )
= ( A + B' ) . ( A' + B )
= ( A.A' ) + ( A.B ) + ( A'B' ) + ( B'.B ) = ( A.B) + (A'B')
= A' ⊕ B
WE CAN SOLVE THIS BY USING TRUTH TABLE :
| A | B | A' | A' xor B | A xnor B |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 |
Now A' ⊕ B = A xnor B
Last updated on May 8, 2025
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