Truth Tables (Cambridge (CIE) IGCSE Computer Science)
Revision Note
Written by: James Woodhouse
Reviewed by: Lucy Kirkham
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 | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
OR
Circuit symbol | Truth Table | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
NOT
Circuit symbol | Truth Table | ||||||
---|---|---|---|---|---|---|---|
|
XOR (exclusive)
Circuit symbol | Truth Table | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
NAND (not and)
Circuit symbol | Truth Table | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
NOR (not or)
Circuit symbol | Truth Table | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
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 (2number 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 | A AND B |
---|---|---|---|
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 | A AND B | NOT 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 | A AND B | NOT 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 |
Examiner Tips and Tricks
It is possible to create a truth table when combining expressions that show only the inputs and the final outputs.
The inclusion of the extra columns supports the process but can be skipped if you feel able to do those in your head as you go.
Last updated:
You've read 0 of your 10 free revision notes
Unlock more, it's free!
Did this page help you?