7. Derived Logic Gates: NAND and NOR (Universal Gates)
NAND and NOR gates are crucial because they are universal gates, meaning any other logic gate (AND, OR, NOT, XOR, XNOR) can be constructed solely using one type of universal gate.
1. The NAND Gate (NOT-AND)
- Function: The inverse of the AND operation.
- Symbol: AND symbol followed by a bubble.
- Equation: $Y = \overline{A \cdot B}$
| A | B | A • B | Y = $\overline{A \cdot B}$ |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
2. The NOR Gate (NOT-OR)
- Function: The inverse of the OR operation.
- Symbol: OR symbol followed by a bubble.
- Equation: $Y = \overline{A + B}$
| A | B | A + B | Y = $\overline{A + B}$ |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |
Universality of NAND
- NOT using NAND: Connect both inputs of a NAND gate together.
- AND using NAND: NAND gate followed by a NOT (NAND).
- OR using NAND: $\overline{(\overline{A}) \cdot (\overline{B})}$ (using De Morgan's Law, covered next).
This universality makes NAND (and NOR) gates highly valuable in integrated circuit (IC) manufacturing.