eolas/Hardware/Logic_Gates/Logic_circuits.md

---
categories:
  - Computer Architecture
  - Electronics
  - Hardware
tags: [logic-gates, binary]
---

# Logic circuits

 > Now that we are familiar with the individual [logic gates](Logic_gates.md) 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. The output of a logic gate is a function of the truth-values of the individual gates and their connections to each other.

## 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)
````

![](../img/../../img/Screenshot_2020-08-31_at_13.52.25.png)

*Line 1 of the truth table*


![](../img/../../img/Screenshot_2020-08-31_at_13.52.34.png)

*Line 2 and 3 of the truth table (equivalent to each other)*


![](../img/../../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/../../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
````

![](../img/../../img/Screenshot_2020-08-31_at_14.12.48.png)

*Automatic door sensor with manual override*
Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`---`
Last Sync: 2022-08-20 12:30:04 2022-08-20 12:30:04 +01:00			`categories:`
Last Sync: 2022-08-21 11:00:04 2022-08-21 11:00:04 +01:00			`- Computer Architecture`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`- Electronics`
Last Sync: 2022-08-20 12:30:04 2022-08-20 12:30:04 +01:00			`- Hardware`
Last Sync: 2022-08-20 15:00:05 2022-08-20 15:00:05 +01:00			`tags: [logic-gates, binary]`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`---`

Last Sync: 2022-07-09 15:30:05 2022-07-09 15:30:05 +01:00			`# Logic circuits`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00
Last Sync: 2022-07-09 15:30:05 2022-07-09 15:30:05 +01:00			`> Now that we are familiar with the individual [logic gates](Logic_gates.md) 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. The output of a logic gate is a function of the truth-values of the individual gates and their connections to each other.`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00
			`## Basic example`

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

Last Sync: 2022-07-09 15:30:05 2022-07-09 15:30:05 +01:00			1. `AND`, `NOT`, `NOT`
Initial commit, pure MD 2022-04-23 13:26:53 +01:00			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)`
			````

Last Sync: 2022-07-09 15:30:05 2022-07-09 15:30:05 +01:00			`![](../img/../../img/Screenshot_2020-08-31_at_13.52.25.png)`

Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`Line 1 of the truth table`

Last Sync: 2022-07-09 15:30:05 2022-07-09 15:30:05 +01:00

			`![](../img/../../img/Screenshot_2020-08-31_at_13.52.34.png)`

Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`Line 2 and 3 of the truth table (equivalent to each other)`
Last Sync: 2022-07-09 15:30:05 2022-07-09 15:30:05 +01:00

			`![](../img/../../img/Screenshot_2020-08-31_at_13.52.42.png)`

Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`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`

Last Sync: 2022-07-09 15:30:05 2022-07-09 15:30:05 +01:00			`Here's a visual representation:`

			`![logic_circuits_5.gif](../img/../../img/logic_circuits_5.gif)`

Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`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`
			````

Last Sync: 2022-07-09 15:30:05 2022-07-09 15:30:05 +01:00			`![](../img/../../img/Screenshot_2020-08-31_at_14.12.48.png)`

Initial commit, pure MD 2022-04-23 13:26:53 +01:00			`Automatic door sensor with manual override`