# Sum of products and k-mapping

Thread Starter

#### Thirsty

Joined Aug 9, 2006
5
I am stuck on a particular problem. I need workout the sum of products and then plot as a k-map. I am confident of the k-map part once i have the sum of products.

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

Any help please?

#### Papabravo

Joined Feb 24, 2006
12,767
There are two ways to do it.

Method #1 Make a function table with three inputs, A, B, and C, and one output call it Y. Fill in the rows with 1's and the sum of products can be written by inspection.
Rich (BB code):
  A  B  C |  Y
---------|---
0  0  0  | 1
0  0  1  | 1
0  1  0  | 1
0  1  1  | 1
1  0  0  | 0
1  0  1  | 1
1  1  0  | 0
1  1  1  | 0

A' + AB'C
Method #2 Algebraic manipulation using DeMorgans Law

Rich (BB code):
(A + B'C)' + (AB + C')'
A'(B'C)'   + (AB)'C            DeMorgan's Law
A'(B + C') + (A' + B')C        Demorgan's Law -- again
A'B  +  A'C'  +  A'C  +  B'C   Distributive Rule
A'B  +  A'(C' +  C)   +  B'C   Distributive Rule and Identity Element
A'(B +  1)    + (A' + A)B'C    Identity Element
A'(B  + 1  + B'C)  + AB'C      Identity Element
A'  + AB'C