Page 62 - Handout Digital Electronics

Rule 1: For two terms two combine and eliminate one variable, they must differ in only one digit
position.

The tabular method makes use of indices. The index in a minterm means the number of binary ones (1s).
Consider the Boolean function: F (A, B, C, D) which can be tabulated as shown below:

A B C D

0 0 0 0 Index 0

0 0 0 1 Index 1

0 0 1 0 Index 1

1 0 1 0 Index 2

1 1 1 0 Index 3

1 1 1 1 Index 4

Examples of minimizing a three variable Boolean function using the tabular method

Example 1

Consider the Boolean function: F (A, B, C) = ABC + ABC + ABC + ABC or F (A, B, C) = ∑ (0, 1, 4,
5)
Step 1

The above function must be changed into binary notation, for example:

F (A, B, C) =∑ (000, 001,100,101)

Step 2

Create List 1 or First List

List 1 is a table showing the function broken down into respective groups using indices. Groups are
separated by horizontal lines.

LIST 1

Index Dec a B C

Group 1 0 0 0 0 0

Group 2 1 1 0 0 1

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