Truth Tables (Cambridge (CIE) O Level Computer Science)

Truth Tables

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 A AND B 0 0 0 0 1 0 1 0 0 1 1 1

OR

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

NOT

Circuit symbol	Truth Table
	A NOT 0 1 1 0

XOR (exclusive)

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

NAND (not and)

Circuit symbol	Truth Table
	A B NOT (A AND B) 0 0 1 0 1 1 1 0 1 1 1 0

NOR (not or)

Circuit symbol	Truth Table
	A B NOT (A OR B) 0 0 1 0 1 0 1 0 0 1 1 0

Truth Tables for Logic Circuits

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)

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

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

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