Page 61 - Handout Digital Electronics

LECTURE 8 THE TABULAR METHOD

8.1 Introduction
The tabular method is also known as the Quine - McCuskey method and is very useful particularly when
dealing with Boolean functions that have large number of variables, for example five, six or more.

This was the first programmable method. The method reduces a function in standard sum of products
(SOP) form to a set of prime implicates from which many variables can be eliminated. The prime
implications are examined to see if some are redundant. The tabular method makes repeated use of the
Boolean law A+ A = 1

This method uses both the binary and decimal notations in the function. In the binary notation, a variable
in true form is denoted by a binary 1, in complement form by a 0 and the absence of a variable by a dash
(-).

8.2 Rules of Tabular Method
Consider a three variable Boolean function F (A, B, C):

ABC is represented by 011, where A= 0, B = 1 and C = 1

ABC is represented by 100, where A=1, B = 0, and C = 0

AC is represented by 1-0, where A = 1, B is absent and C = 0

BC is represented by -11, where A is absent, B = 1 and C = 1

Consider the Boolean function:

F (A, B, C, D) =∑ (1110, 1111) = ABCD + ABCD = ABC
The two minterms can be listed and combined as shown:

A B C D

1 1 1 0 Can combine because they differ in one digit position.

1 1 1 1

1 1 1 -

Consider the following Boolean function:

F (A, B, C, D) =∑ (1101, 1110) = ABCD + ABCD
These minterms can also be listed as:

A B C D

1 1 0 1 cannot combine because they differ in more than one digit

1 1 1 0 position

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