notes/education/computer engineering/ECE2700/Binary Logic.md

![](./assets/logic-gates.jpeg)
# NOT Gate
A binary NOT gate has a single input, and inverts that input.

## Truth Table
| $x$ | $y$ |
| --- | --- |
| 0   | 1   |
| 1   | 0   |
## Mathematical Expression
A NOT operation is mathematically expressed using a bar:
$$ y = \bar{x} $$
# AND Gate
An AND gate will only output a 1 if *both* inputs are a one.

## Truth Table
| $x_1$ | $x_2$ | $y$ |
| ----- | ----- | --- |
| 0     | 0     | 0   |
| 0     | 1     | 0   |
| 1     | 0     | 0   |
| 1     | 1     | 1   |
## Mathematical Expression
An AND operation is mathematically expressed using a times symbol, or with no symbol at all
$$ y = x_1 \cdot x_2 = x_1x_2$$

# NAND Gate
A NAND gate outputs a 1 *unless* both inputs are enabled.

## Truth Table
|