Question
Download Solution PDFThe output Y of the logic circuit given below is:-
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFXOR GATE
Symbol:
Truth Table:
|
Input A |
Input B |
Output Y = A ⊕ B |
|
0 |
0 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
Output Equation: \(Y = {\bf{A}} \oplus {\bf{B}} = \bar AB + A \bar B\)
Key Points:
1) If B is always High, the output is the inverted value of the other input A, i.e. A̅.
1) The output is low when both the inputs are the same.
2) The output is high when both the inputs are different.
Explanation:
\(Y = {\bf{\bar X}} \oplus {\bf{X}} = \bar{\bar X} X+\bar X \bar X\)
\(Y = XX+\bar X \bar X\)
\(Y = X+\bar X \)
Y = 1
|
Name |
AND Form |
OR Form |
|
Identity law |
1.A=A |
0+A=A |
|
Null Law |
0.A=0 |
1+A=1 |
|
Idempotent Law |
A.A=A |
A+A=A |
|
Inverse Law |
AA’=0 |
A+A’=1 |
|
Commutative Law |
AB=BA |
A+B=B+A |
|
Associative Law |
(AB)C |
(A+B)+C = A+(B+C) |
|
Distributive Law |
A+BC=(A+B)(A+C) |
A(B+C)=AB+AC |
|
Absorption Law |
A(A+B)=A |
A+AB=A |
|
De Morgan’s Law |
(AB)’=A’+B’ |
(A+B)’=A’B’ |
Last updated on Apr 11, 2023