---
tags:
  - Theory_of_Computation
  - Logic
  - Electronics
  - binary
---


 > 
 > Now that we are familiar with the individual logic gates and their truth conditions we are in a position to create **logic circuits**. These are combinations of logic gates controlled by inputs that can provide a range of useful outputs.

## Basic example

In the below circuit we have the following gates connected to two inputs with one output, moving through the following stages:

1. `AND`, `NOT` , `NOT`
1. `AND`, `NOR`

This is equivalent to the following truth table:

````
A    B   Output
_    _   _____

0    0     0       (1)
1    0     1       (2)
0    1     1       (3)
1    1     0       (4)
````

![Screenshot_2020-08-31_at_13.52.25.png](../img/Screenshot_2020-08-31_at_13.52.25.png)
*Line 1 of the truth table*

![Screenshot_2020-08-31_at_13.52.34.png](../img/Screenshot_2020-08-31_at_13.52.34.png)
*Line 2 and 3 of the truth table (equivalent to each other)*
![Screenshot_2020-08-31_at_13.52.42.png](../img/Screenshot_2020-08-31_at_13.52.42.png)
*Line 4 of the truth table*

## Applied example

With this circuit we have a more interesting applied example.

It corresponds to an automatic sliding door and has the following states

* a proximity sensor that opens the doors when someone approached from outside
* a proximity sensor that opens the doors when someone approaches from the inside
* a manual override that locks both approaches (inside and out) meaning no one can enter of leave

Here's a visual representation:!
[logic_circuits_5.gif](../img/logic_circuits_5.gif)
The following truth table represents this behaviour, with A and B as the door states, C as the override and X as the door action (0 = open, 1 = closed)

````
A  B  C  X
_  _  _  _

0  0  0  0      
1  0  0  0     
0  1  0  0     
1  1  0  0
0  0  1  0
1  0  1  1
0  1  1  1
1  1  1  1
````

![Screenshot_2020-08-31_at_14.12.48.png](../img/Screenshot_2020-08-31_at_14.12.48.png)
*Automatic door sensor with manual override*