Page 38 - Handout Digital Electronics

LECTURE 5 TRUTH TABLES

5.1 Introduction

A truth table, in Boolean algebra is a table used to calculate the functional value of a Boolean function
or expression on each of the Boolean variables. The truth tables are used to show or tell whether a
Boolean function returns a 1 (true) or a 0 (false) for all the valid input values. Truth tables are popular
with logic gates, combinational and sequential circuits. This is because it does not matter how complex
a Boolean function is, the final output value computes to a 1(true) or 0 (false) value. A truth table is
made up of columns for each input variable, for example (for example, A, and B) and one final (output)
column for all the possible outputs (results) of the logical operation the truth table is meant to
represent for example for the function: F = A+B, truth table will appear as shown in table 1 below:

Input Variables Output
A B F
0 0 0
0 1 1
1 0 1
1 1 1

Table 1: Truth table for Boolean function F= A + B

A and B are the two Boolean variables and F is the output. The values under columns A and B are
known as possible input combinations and those under column F are called possible results for each
input combination for A and B. If only one Boolean variable is used, the truth table has only two
columns, one column for variable and another for the results (output). The possible input combinations
for one Boolean variable are two and the outputs are also two. See table below the Boolean function F
= A:

Table 2: Truth table for the Boolean function F = A

Input Output
A F
0 0
1 1

If a Boolean function has three (3) variables, then there are three input columns and one output
(results) column. There are eight possible input combinations and eight possible results that is one for
each input combination. To calculate the number of possible input combinations, raise the number of
1
2
input variables as a power of two for example for one input variable, 2 = 2, for two input variables 2 =
3
4
4 and for three input variables, 2 = 8, and for four inputs, 2 = 16. In this module only Boolean
functions with four variables will be used. The table below shows a three variable truth table:

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