eolas/Hardware/Logic_Gates/Logic_circuits.md

tags
Logic Electronics binary

Logic circuits

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. 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
2. 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)

Line 1 of the truth table

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

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:

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

Automatic door sensor with manual override