# Sum of products and k-mapping

Discussion in 'Homework Help' started by Thirsty, Sep 21, 2006.

1. ### Thirsty Thread Starter New Member

Aug 9, 2006
5
0
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')'

2. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
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.
Code ( (Unknown Language)):
1.
2.   A  B  C |  Y
3. ---------|---
4.   0  0  0  | 1
5.   0  0  1  | 1
6.   0  1  0  | 1
7.   0  1  1  | 1
8.   1  0  0  | 0
9.   1  0  1  | 1
10.   1  1  0  | 0
11.   1  1  1  | 0
12.
13. A' + AB'C
14.
15.
Method #2 Algebraic manipulation using DeMorgans Law

Code ( (Unknown Language)):
1.
2. (A + B'C)' + (AB + C')'
3. A'(B'C)'   + (AB)'C            DeMorgan's Law
4. A'(B + C') + (A' + B')C        Demorgan's Law -- again
5. A'B  +  A'C'  +  A'C  +  B'C   Distributive Rule
6. A'B  +  A'(C' +  C)   +  B'C   Distributive Rule and Identity Element
7. A'(B +  1)    + (A' + A)B'C    Identity Element
8. A'(B  + 1  + B'C)  + AB'C      Identity Element
9. A'  + AB'C
10.