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The problem I need help with is the following.:

1. The problem statement, all variables and given/known data

"Simplify to obtain minimum SOP.

F(A, B, C, D) = A’B’CD’+AC’D’+ABC’+AB’C+AB’C+BC’D"

The problem stated above has two provided solutions, the "main" one and the "alternate" one.

I'm confused with both of them.

Here they are (within this post directly and indirectly within a PDF, since some people prefer it directly here, but I think it looks better in the pdf).:

"Main" solution:

("*"s are used for preserving formatting)

A’B’CD’ + AC’D’ + ABC’ + AB’C + AB’C + BC’D

*2*********8,12****12,13**10,11**10,11***5,13

...*******************ABC'(D+D')*************ABC' is deleted (There is an arrow going from AC'D' on the line above to the left whitespace of ABC'(D+D'), on this line. There is also another arrow going from BC'D to ABC'(D+D') (from the left - not that I think that the direction from which it's coming matters).)

2 & 10,11**A'B'CD' + AB'C = B'C(A+A'D)

Final result: B'CD' + AC'D' + AB'C + BC'D

"Alternate" solution:

= A’B’CD’ + AC’D’ + ABC’ +AB’C + AB’C + BC’D

= A’B’CD’ + (C’D’ + BC’ + B’C)A + BC’D

= A(CC’+B’C) + BC’D + A’B’CD’

= AC’D’ +A’B’CD’ +AB’C +BC’D

= AC’D’ + B’CD’+AB’C + BC’D

PDF version of "main" and "alternate" solutions (The problem is problem 1a.):

https://www.docdroid.net/PacYXo3/1a-main-solution-and-alternate-solution.pdf

2. Relevant equations

A + 1 = 1 Annulment

A + 0 = A Identity

A + 0 = A Identity

A ⋅ 1 = A Identity

A ⋅ 0 = 0 Annulment

A + A = A Idempotent

A ⋅ A = A Idempotent

(A')' Double Negation

A + A' = 1 Complement

A ⋅ A' = 0 Complement

A+B = B+A Commutative

A⋅B = B⋅A Commutative

(A+B)' = A' ⋅ B' de Morgan’s Theorem

(A⋅B)' = A' + B' de Morgan’s Theorem

Source:

https://www.electronics-tutorials.ws/boolean/bool_6.html

3. The attempt at a solution

When I tried to follow the logic of the solutions, I encountered some problems.

Here they are.:

For the main solution of Q1 a):

1)

What are the numbers 2, 8, 12, 12, 13, 10,11, 10,11, 5, 13?

2)

What is meant by ABC’ is deleted? Is what is meant (D + D’) is “deleted”?

3)

What is done on the before-last linute to get to the last line / line with text “Final Result:”?

For the alternate solution of Q1 a):

4)

How does one go from (C’D’ + BC’ + B’C)A to A(CC’+B’C)?

5)

How does one go from A(CC’+B’C) to AC’D’ +AB’C?

6)

How does the A’B’CD’ become B’CD’ from the before-last line to the last line?

Any input would be greatly appreciated!

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# Boolean Algebra, Minimum Sum of Products Problem

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