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Logic Gate Truth Tables - Reference Guide (Cheat Sheet)

A logic gate is the implementation of a Boolean function. It performs a logic operation on one or more binary input. By binary I mean that the input can either be 1 or 0, nothing else.
This guide is intended to be quick guide\reference, I will dive into more details about each gate on transistor\diode level in other posts.

The guide cover gates with 2 inputs, meaning that each truth table will have 4 cases (2^2 = 4)


AND Gate:
Boolean Logic Operator: Q = A • B 

Input Output
A B Q
0 0 0
0 1 0
1 0 0
1 1 1
Summary: in order to achieve 1 on the output, both inputs A AND B must be 1


OR Gate:
Boolean Logic Operator: Q = A + B 

Input Output
A B Q
0 0 0
0 1 1
1 0 1
1 1 1
Summary: in order to achieve 1 on the output, input A OR input B must be 1


NOT Gate (Inverter):
Boolean Logic Operator: Output will be A'

Input | Output
A A'
0 1
1 0
Summary: whatever is on the input will be inverted on the output. HIGH (1) will become LOW (0) and vice versa.


Buffer Gate:

Boolean Logic Operator: Output will be the same as Input

Input | Output
A A
0 0
1 1
Summary: whatever is on the input, will be the same on output


NAND Gate:
Boolean Logic Operator: Q = (A • B)' 

The NAND gate is pretty much AND with its output connected to a NOT gate like in the figure below:

Input Output
A B Q
0 0 1
0 1 1
1 0 1
1 1 0
Summary: in order to achieve 0 on the output, both inputs must be 1


NOR Gate:
Boolean Logic Operator: Q = (A + B)' 

The NOR gate is pretty much OR with its output connected to a NOT gate like in the figure below:

Input Output
A B Q
0 0 1
0 1 0
1 0 0
1 1 0
Summary: in order to achieve 1 on the output, both inputs must be 0
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