DeMorgan's Laws
De Morgan's laws are indispensable in digital electronics. The laws
outlined by him are simple to understand, yet transformed the Boolean algebra in
a dramatic way.
First Law
A + B = A.B
Proof:
| Left-hand-side |
| A | B | A+B | A + B |
| 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
| Right-hand-side |
| A | B | A | B | A.B |
| 1 | 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
Second Law
A.B = A + B
Proof:
| Left-hand-side |
| A | B | A.B | A.B |
| 1 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
| Right-hand-side |
| A | B | A | B | A + B |
| 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
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