Karnaugh map?

Question

Simplify the Boolean function using 5 variable Kmap:
F(A,B,C,D,E) = E (0,2,4,6,9,13,21,23,25,29,31)
(Note : E refers to Sigma)

Please help!

Answer 1

First, break down each of your numbers into their binary representation:
0 = 00000 --> A'B'C'D'E'
2 = 00010 --> A'B'C'DE'
4 = 00100 --> A'B'CD'E'
6 = 00110 --> A'B'CDE'
9 = 01001 --> A'BC'D'E
13 = 01101 --> A'BCD'E
21 = 10101 --> AB'CD'E
23 = 10111 --> AB'CDE
25 = 11001 --> ABC'D'E
29 = 11101 --> ABCD'E
31 = 11111 --> ABCDE

Then graph them into a 5-variable karnaugh map. I've attached an image.

Then group the variables. For example the four values (0,2,4,6) shown in red become a single group = A'D'E'

The values in green (21,23,29,31) are grouped as ACE

Finally the values in blue (9, 13, 25, 29) are grouped as AB'D

The simplified solutions is therefore:
A'D'E' + ACE + AB'D

Answer 2

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