Truth Tables (AQA GCSE Computer Science)

What is a truth table?

• A truth table is a tool used in logic and computer science to visualise the results of Boolean expressions
• They represent all possible inputs and the associated outputs for a given Boolean expression

AND 

Circuit symbol	Truth Table
	A B 0 0 0 0 1 0 1 0 0 1 1 1

OR

Circuit symbol	Truth Table
	A B 0 0 0 0 1 1 1 0 1 1 1 1

NOT

Circuit symbol	Truth Table
	A 0 1 1 0

XOR (exclusive)

Circuit symbol	Truth Table
	A B 0 0 0 0 1 1 1 0 1 1 1 0

How do you create truth tables for logic circuits?

• To create a truth table for the expression P = (A AND B) AND NOT C // 
  • Calculate the numbers of rows needed (2^{number of inputs})
  • In this example there are 3 inputs (A, B, C) so a total of 8 rows are needed (2³)
  • To not miss any combination of inputs, start with 000 and count up in 3-bit binary (0-7)

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

• • Add a new column to show the results of the brackets first (A AND B // )

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

• • Add a new column to show the results of NOT C // 

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

• • The last column shows the result of the Boolean expression (P) by comparing (A AND B) AND NOT C // 

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