Convert Standard SOP to Minimal SOP form

In this tutorial, you will learn how to convert any boolean expression given to you in standard or canonical Sum of Products (SOP) form to minimal Sum of Products (SOP) form.

However, before we get started, here is a list of two articles that are connected to this post and should be read in conjunction with it. You might be interested in reading the following articles:

• Sum of Product (SOP)
• SOP to Standard SOP

The minimal SOP form contains the shortest product term (with the fewest literals) and provides the same comprehensive information as the standard SOP form.

Let's take a look at an example that demonstrates how the standard SOP form can be converted into the minimal SOP form. The following is the form of the given boolean expression using the standard SOP notation:

A'BC' + AB'C' + AB'C + ABC' + ABC

Now let's convert it into minimal SOP form:

F = A'BC' + AB'C' + AB'C + ABC' + ABC
= A'BC' + AB'(C+C') + AB(C+C')      [∵ ABC + ABD = AB(C+D)]
= A'BC' + AB' + AB                  [∵ A'+A = 1]
= A'BC' + A(B'+B)
= A'BC' + A

Let BC' be X. Therefore, the equation becomes,

= A'X + A
= A + A'X        [∵ A+B=B+A]
= A + X          [∵ A+A'B=A+B]

Now, putting the value of X in the above equation, we get,

= A + BC'

And this is the final SOP form, which is called the minimal SOP form. The complete function is written as,

F = A + BC'

Another article that you could find interesting to read is as follows: Standard POS to Minimal POS. This article can also be found in an upcoming post.

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