eolas/Theory_of_Computation/Logic_circuits.md

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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
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:! 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

Automatic door sensor with manual override