Simplifying Boolean Function using K-Map -Special Case

K-Map technique is a straight forward and simple method for minimizing Boolean functions. In this article, you will learn a special case of K-map, when the function is in a Standard Sum of Product and not in a Canonical Sum of Product form.

For example

  F = A'B'C' + ABC'            -  (1)    F = A'B + BC' + A'B          -  (2)  

In function1, each term is called a minterm( A’B’C). The sum of minterms is called a Canonical Sum of Product. It can be directly taken from the Truth Table for the function.

The function2 has terms called a product term which may have one or more literal. The sum of all such terms is called a Standard Sum of Product.

The same concept applies for Canonical Product of Sum form.

Now the problem is that if you are given a Standard Sum of Product for Boolean minimization, what to do, because it appears that its already minimized.

How to simplify the function 2 using K-Map?

Create a three variable map like we do always .and put 1 in the box where a particular term is missing .

  A'B  

Which term is missing ? yes right!  it’s C

A'B( C + C')  A'BC + A'BC'

In the map you put 1 in the cell for both

A'BC + A'BC'

.

Similarly, Solve other missing variable in each of the terms of the function.

KMAP for F = A'B + BC' + A'B
KMAP for F = A’B + BC’ + A’B

Now , you can minimize the above 3-variable K-Map easily because you have identified the correct boxes.

 

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