About Truth table

Truth table


The truth table is an important part of the digital electronics discussion. We get different truth tables from each type of logical gates. 


In Boolean algebra logic circuits have multiple inputs and only a single output. Combining these inputs and outputs we can make a table for understanding the combinations between them. This table is called the truth table.


Let us have n variables. From these n variables, we have a 2ⁿ number of inputs.

Let us have two variables X and Y. From these two inputs, we have 2² = 4 inputs.

Number of
Variables (n)
Number of
Inputs(2ⁿ)
2
2²=4
3
2³=8

Remember that value of the inputs either 0 or 1.

Structure for two inputs

For 2 inputs the truth table will be like this  

Inputs
Outputs
X
Y
R(Depends on
 logical gates)
0
0

0
1

1
0

1
1



Structure for three inputs 

For 3 inputs the truth table will be like this 

Inputs
Outputs
X
Y
Z
R(Depends on
 logical gates)
0
0
0

0
0
1

0
1
0

0
1
1

1
0
0

1
0
1

1
1
0

1
1
1


Expressions outputs are easily made comparable by the Truth table. After drawing a circuit with its logical expression we can write a truth table for understanding the outcomes from the inputs.

We have to use truth tables in a lot of cases in digital electronics such as in showing Encoder, Decoder probable outputs showing.

Read about De Morgan's law.