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education/computer engineering/ECE2700/Binary Logic.md
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![](./assets/logic-gates.jpeg) ![](./assets/logic-gates.jpeg)
# NOT Gate # NOT Gate
A binary NOT gate has a single input, and inverts that input. A binary NOT gate has a single input, and inverts that input (output is not the input).
## Truth Table ## Truth Table
| $x$ | $y$ | | $x$ | $y$ |
@ -12,7 +12,7 @@ A binary NOT gate has a single input, and inverts that input.
A NOT operation is mathematically expressed using a bar: A NOT operation is mathematically expressed using a bar:
$$ y = \bar{x} $$ $$ y = \bar{x} $$
# AND Gate # AND Gate
An AND gate will only output a 1 if *both* inputs are a one. An AND gate will only output a 1 if *both* inputs are a one (input one *and* input two are enabled).
## Truth Table ## Truth Table
| $x_1$ | $x_2$ | $y$ | | $x_1$ | $x_2$ | $y$ |
@ -26,7 +26,7 @@ An AND operation is mathematically expressed using a times symbol, or with no sy
$$ y = x_1 \cdot x_2 = x_1x_2$$ $$ y = x_1 \cdot x_2 = x_1x_2$$
# NAND Gate # NAND Gate
A NAND gate outputs a 1 *unless* both inputs are enabled. A NAND gate outputs a 1 *unless* both inputs are enabled (input one *and* input two are *not* enabled).
## Truth Table ## Truth Table
| $x_1$ | $x_2$ | $y$ | | $x_1$ | $x_2$ | $y$ |
@ -41,7 +41,7 @@ $$ y = \overline{x_1 \cdot x_2}$$
# OR Gate # OR Gate
An OR gate outputs a 1 if either or both inputs are enabled. An OR gate outputs a 1 if either or both inputs are enabled (if input one *or* input two is enabled).
## Truth Table ## Truth Table
| $x_1$ | $x_2$ | $y$ | | $x_1$ | $x_2$ | $y$ |
| ----- | ----- | --- | | ----- | ----- | --- |
@ -53,3 +53,6 @@ An OR gate outputs a 1 if either or both inputs are enabled.
A mathematical OR is notated with a $+$ symbol. A mathematical OR is notated with a $+$ symbol.
$$ y = x_1 + x_2 $$ $$ y = x_1 + x_2 $$
# NOR Gate
A NOR gate outputs a one if neither gate is enabled.