Topics / Boolean Logic / Logic Gates

# Logic Gates

Logic gates are the building blocks of a digital circuit.

Every terminal in a logic gate will always be in one of the two binary states (0) or (1).

These binary states represent the presence (1), or absence (0), of an electrical voltage. Binary (1) can be referred to as positive or ON, whilst binary (0) can be called negative or OFF.

There are many types of logic gates, each with their own characteristics.

Our Logic Circuits page explains how these gates can be placed together to form circuits.

## The Logic Gates

NameSymbolExplanationNotation
NOT Inverses the current output, therefore positive (1 or ON) becomes negative (0 or OFF), whilst negative (0 or OFF) would become positive (1 or ON). Z = NOT A
AND Both inputs have to be positive (1) before the output is also positive (1). Z = A AND B
OR At least one input has to be positive (1) to give a positive output (1 or ON).  Both inputs could also be positive. Z = A OR B
NAND NOT AND.  The same as AND, but then inverse (NOT) the outcome.  So, perform AND first, then apply a NOT to the output. Z = A NAND B
NOR NOT OR.  The same as OR, but then inverse (NOT) the outcome.  So, perform OR first, then apply a NOT to the output. Z = A NOR B
XOR Exclusive OR. Only one input is allowed to be positive (1 or ON) to give a positive output (1).  If both inputs are positive (1) then there is a negative outcome (0, or OFF). Z = A XOR B

Test your logic gate knowledge with our quick quiz.

## Logic Gate Truth Tables

Truth tables are used to calculate the output from a logic gate or circuit.

Every possible binary input combination is covered in a truth table.  From this, we can clearly see what the output would be in any scenario.

Input AOutput Z
01
10

## AND

### AND gate truth table

Input AInput BOutput Z
000
010
100
111

## OR

### OR gate truth table

Input AInput BOutput Z
000
011
101
111

## NAND

### NAND gate truth table

Input AInput BOutput Z
001
011
101
110

## NOR

### NOR gate truth table

Input AInput BOutput Z
001
010
100
110

## XOR

### XOR gate truth table

Input AInput BOutput Z
000
011
101
110

Test your knowledge of truth tables with our quick quiz.

Topics / Boolean Logic / Logic Gates