Computer Science
State the distributive law. Verify it using the truth table.
Boolean Algebra
59 Likes
Answer
This law states that:
- A(B + C) = A.B + A.C
- A + BC = (A + B).(A + C)
Truth Table of first law
| A | B | C | B+C | A.(B+C) | A.B | A.C | A.B+A.C |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Truth Table of second law
| A | B | C | BC | A+BC | A+B | A+C | (A+B).(A+C) |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Answered By
29 Likes
Related Questions
Simplify the following expression and convert it into its canonical POS form:
(X.Y + Z)(Y + Z'.X)What is the Canonical form of Boolean expression? State the two types of Canonical forms.
Minimise the following expression. At each step clearly mention the law used.
Y.(A+B').(B+CD)'Verify that:
(Z + X)(Z + X' + Y) = (Z + X)(Z + Y)