5. Introduction to Boolean Algebra
Boolean algebra, developed by George Boole, is the mathematical foundation of digital logic. It deals with variables that can only have two states: True (1) or False (0).
Boolean Variables and Constants
- Variables: Represented by letters (A, B, X, Y), they hold a value of 0 or 1.
- Constants: The fixed values 0 (False) and 1 (True).
Basic Boolean Operations
There are three fundamental operations:
1. OR Operation (Logical Addition)
Symbol: + or OR
Output is 1 if at least one input is 1.
| A | B | A + B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
2. AND Operation (Logical Multiplication)
Symbol: • or AND
Output is 1 only if all inputs are 1.
| A | B | A • B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
3. NOT Operation (Inversion or Complement)
Symbol: $\overline{A}$ or $A'$ Inverts the input (0 becomes 1, 1 becomes 0).
| A | $\overline{A}$ |
|---|---|
| 0 | 1 |
| 1 | 0 |