Digital Logic - Old Questions
5. Proof the De-Morgan 1st and 2nd theorem with truth table and logic gates.
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 |
