Truth table

A truth table is just a way of us showing all the possible outputs of a logical operation (or logic gate) based on all the possible combinations of its inputs.

An example: AND

For example, let’s consider a simple logical operation called “AND”. The AND operation takes two inputs and produces an output that is “true” (or “1”) only if both inputs are “true” (or “1”). If either input is “false” (or “0”), the output is also “false” (or “0”).

If we list out all the possible combinations of inputs and their corresponding outputs, we get the following truth table for the AND operation:

Input A	Input B	Output (A AND B)
0	0	0
0	1	0
1	0	0
1	1	1

In this table:

• The first column represents the first input (Input A).
• The second column represents the second input (Input B).
• The third column shows the output of the AND operation based on the values of Input A and Input B.

Interpreting truth tables

Let’s take the example from above:

Input A	Input B	Output (A AND B)
0	0	0
0	1	0
1	0	0
1	1	1

• In the first row, both inputs are 0, so the output is 0 (because A AND B is false).
• In the second row, Input A is 0 and Input B is 1, so the output is still 0 (because A AND B is false).
• In the third row, Input A is 1 and Input B is 0, so the output is again 0 (because A AND B is false).
• In the fourth row, both inputs are 1, so the output is 1 (because A AND B is true).

So we can see that, for an AND gate to output a 1, both of its inputs must be 1.

Truth tables with only one input

Here’s an example of a truth table for a logical operation called “NOT”, which takes a single input and produces an output that is the opposite of the input.

It works in exactly the same way:

Input A	Output (NOT A)
0	1
1	0

How about 3 inputs?

Here’s a truth table for a logical operation which outputs a 1 if at least two of its three inputs are 1:

Input A	Input B	Input C	Output
0	0	0	0
0	0	1	0
0	1	0	0
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	1
1	1	1	1

In this table, the output is 1 in the rows where at least two of the inputs are 1.

That’s all there is to truth tables! They’re just a simple way of showing how logical operations work based on their inputs.