Digital Logic - Old Questions
Question Answer Details
6. Proof the 1st and 2nd law of De Morgan’s theorems with logic gate and truth table.
Answer
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Official Answer
De-Morgans Theorem
De Morgan’s theorem is used to convert OR type of expression into AND type and vice-versa.It is further divided into two different types;
1st law:
It state that the total complement of sum is equal to the product of individual complement. i.e. (A+B)’=A’ ٠B’
Proof:
Input | Output | ||
A | B | (A+B)’ | A’ ٠B’ |
0 | 0 | 1 | 1 |
0 | 1 | 0 | 0 |
1 | 0 | 0 | 0 |
1 | 1 | 0 | |
2nd law:
It state that the total complement of the product is equal to the sum of individual complement. i.e. (A٠B)’ =A’+B’
Proof:
Input | Output | ||
A | B | (A٠B)’ | A’+B’ |
0 | 0 | 1 | 1 |
0 | 1 | 1 | 1 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
