56 lines
1.3 KiB
Markdown
56 lines
1.3 KiB
Markdown
|
|
|
|
# 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
|
|
| $x_1$ | $x_2$ | $y$ |
|
|
| ----- | ----- | --- |
|
|
| 0 | 0 | 1 |
|
|
| 0 | 1 | 1 |
|
|
| 1 | 0 | 1 |
|
|
| 1 | 1 | 0 |
|
|
## Mathematical Expression
|
|
A NAND operation is mathematically expressed using a bar over an AND operation:
|
|
$$ y = \overline{x_1 \cdot x_2}$$
|
|
|
|
|
|
# OR Gate
|
|
An OR gate outputs a 1 if either or both inputs are enabled.
|
|
## Truth Table
|
|
| $x_1$ | $x_2$ | $y$ |
|
|
| ----- | ----- | --- |
|
|
| 0 | 0 | 0 |
|
|
| 0 | 1 | 1 |
|
|
| 1 | 0 | 1 |
|
|
| 1 | 1 | 1 |
|
|
## Mathematical Expression
|
|
A mathematical OR is notated with a $+$ symbol.
|
|
|
|
$$ y = x_1 + x_2 $$
|