Page 39 - Handout Digital Electronics

Table 3: A three variable Boolean function truth table

Input variables Output
A B C F
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 1

The results (outputs) in column F can be given arbitrary and do not worry about how they have been
computed) calculated. There is a chapter devoted to the calculations of the outputs of Boolean
functions.

5.2 Forms of Boolean Expressions

Consider the numeric representation of a Boolean function given in a three variable table below:

Table 4: Three variable truth table

Dec A B C F
0 0 0 0 1
1 0 0 1 0
2 0 1 0 0
3 0 1 1 1
4 1 0 0 0
5 1 0 1 1
6 1 1 0 1
7 1 1 1 0

In the above truth table, Dec values are the decimal values, that is base ten representations, A, B, C are
the Boolean variables, and F is the output (result).The input combinations of A.B and C are listed in
ascending order from 000 to 111. This does not necessarily mean that the function operates in this
order but rather the ascending order is used so that no input combination can be mistakenly left out.

Looking at the truth table, the function F has a value of 1 for the following input combinations: 000,
011,101, and 110. This can be written as: F (A, B, C) = ABC ABC ABC ABC
. The (A, B, C) in parenthesis are used to show that the function is three variables.

This function can also be written as: F (A, B, C) = 000+011+101+110. This can still further be reduced to
the form: F (A, B, C) = ∑ (000, 011, 101, 110). This form can further be written in a more convenient
decimal form: F (A, B, C) =∑ (0, 3, 5, 6).

39