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education/computer engineering/ECE2700/Binary Logic.md
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@ -38,9 +38,17 @@ Given the below truth table, synthesize a boolean expression that corresponds.
| 0 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
- $f(0, 0)$ evaluates to true with the term $\overline{x}_1 \cdot \overline{x}_2$
- $f(0, 1)$ evaluates to true with the term $\overline{x}_1\cdot x_2$
- $f(0, 0)$ evaluates to true with the expression $\overline{x}_1 \cdot \overline{x}_2$
- $f(0, 1)$ evaluates to true with the expression $\overline{x}_1\cdot x_2$
- $f(1, 0)$ should provide an output of zero, so that can be ignored
- $f(1, 1)$ evaluates to true with the expression $x_1 \cdot x_2$
ORing all of the above expression together, we get:
$$ f(x_1, x_2) = \overline{x}_1\overline{x}_2 + \overline{x}_1 x_2 + x_1x_2 $$
$$
\begin{equation}
= x_1 \\
\end{equation}
$$
# Logic Gates
![](./assets/logic-gates.jpeg)