Prove De-Morgan's Law Using Truth Table Answer With Hand Written Notes [Digital Electronics]
(2.) Prove De-Morgan's Law Using Truth Table. [KU - 2018]
ANS: De-Morgan's First Law :
The first theorem of De Morgan's Law defines that the inverted result from AND Operation is the same as the OR operation of a complement of each variable where the Result equal NAND Operation.
De-Morgan's First Law Formula :
(X•Y)' = X' + Y'
De-Morgan's First Law Truth Table
| X | Y | X' | Y' | X•Y | (X•Y)' | X'+Y' |
|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 0 | 0 |
De-Morgan's Second Law :
The Second theorem of De Morgan's Law defines that the inverted result from OR Operation is the same as the AND operation of a complement of each variable where the Result equal NOR Operation.
De-Morgan's Second Law Formula :
(X+Y)' = X' • Y'
De-Morgan's Second Law Truth Table
| X | Y | X' | Y' | X+Y | (X+Y)' | X'•Y' |
|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 | 0 |
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