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education/computer engineering/ECE2700/Binary Logic.md
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@ -22,11 +22,20 @@ An AND gate will only output a 1 if *both* inputs are a one.
| 1 | 0 | 0 |
| 1 | 1 | 1 |
## Mathematical Expression
An AND operation is mathematically expressed using a times symbol, or with no symbol at all
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:
$$ y = \overline{x_1 \cdot x_2}$$