Logic Gates

Logic gates

Electronic circuits in computers, many memories and controlling devices are made up of thousands of logic gates.
Logic gates take binary inputs and produce a binary output.
Several logic gates combined together form a logic circuit and these circuits are designed to carry out a specific function.
The checking of the output from a logic gate or logic circuit can be done using a truth table.

NOT gate

Description

The output, X, is 1 if the input A is NOT 1

How to write this

X = NOT A (logic notation)
$X = \overline{A}$ (Boolean algebra)

Truth table

Input	Output
A	X
0	1
1	0

AND gate

Description

The output, X, is 1 if input A is 1 and input B is 1

How to write this

X = A AND B (logic notation)
$X = {A \cdot B}$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	0
0	1	0
1	0	0
1	1	1

OR gate

Description

The output, X, is 1 if input A is 1 or input B is 1.

How to write this

X = A OR B (logic notation)

$X = A + B$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	0
0	1	1
1	0	1
1	1	1

NAND gate

Description

The output, X, is 1 if input A is NOT 1 or input B is NOT 1.

How to write this

X = A NAND B (logic notation)

$X = \overline{A \cdot B}$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	1
0	1	1
1	0	1
1	1	0

NOR gate

Description

The output, X, is 1 if: input A is NOT 1 and input B is NOT 1

How to write this

X = A NOR B (logic notation)

$X = \overline{A + B}$ (Boolean algebra)

Truth table

Input	Input	Output
A	B	X
0	0	1
0	1	0
1	0	0
1	1	0

XOR gate

Description

The output, X, is 1 if (input A is 1 AND input B is NOT 1) OR (input A is NOT 1 AND input B is 1)

How to write this

X = A XOR B (logic notation)
$X = ({A \cdot \overline{B}}) + ({\overline{A} \cdot B})$ (Boolean algebra)

(Note: this is sometimes written as: $(A + B) \cdot \overline{(A \cdot B )}$)

Truth table

Input	Input	Output
A	B	X
0	0	0
0	1	1
1	0	1
1	1	0

Logic circuits 1

Produce a truth table for the following logic circuit

Complete the truth table for the logic circuit.

A	B	C
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

[0/4]

Logic circuits 2

A safety system uses three inputs to a logic circuit. An alarm, X, sounds if input A represents ON and input B represents OFF, or if input B represents ON and input C represents OFF.
Produce a logic circuit and truth table to show the conditions which cause the output X to be 1.

Logic statement

X = 1 if (A = 1 AND B = NOT 1) OR (B = 1 AND C = NOT 1)

this equates to A is ON and B is OFF
this equates to B is ON AND C is OFF

Boolean algebra

$X = ({A \cdot \overline{B}}) + ({B} \cdot \overline{C})$

Draw the logic circuit for the logic expression:

X = (A AND B) OR (NOT ((A AND C) AND (B OR C))).

[0/1]

Logic circuits 3

A wind turbine has a safety system which uses three inputs to a logic circuit. A certain combination of conditions results in an output, X, from the logic circuit being equal to 1. When the value of X = 1, the wind turbine is shut down.
- either turbine speed ≤ 1000 rpm and bearing temperature > 80 °C
- or turbine speed > 1000 rpm and wind velocity > 120 kph
- or bearing temperature ≤ 80 °C and wind velocity > 120 kph
The following table shows which parameters are being monitored and form the three inputs to the logic circuit.
The output, X, will have a value of 1 if any of the following combination of conditions occur:

Parameter description	Parameter	Binary value	Description of condition
turbine speed	S	0	turbine speed ≤ 1000 rpm
turbine speed	S	1	turbine speed > 1000 rpm
bearing temperature	T	0	bearing temperature ≤ 80 °C
bearing temperature	T	1	bearing temperature > 80 °C
wind velocity	W	0	wind velocity ≤ 120 kph
wind velocity	W	1	wind velocity > 120 kph