Page 65 - Handout Digital Electronics
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Example 3
Minimize the Boolean function below using the tabular method:
F(A, B, C, D) =∑(1,3,5,7,8,9,10,11,12,13,14,15)
Convert the decimal numbers to binary as follows:
F (A, B, C, D) =∑ (0001, 0011, 0101, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1101, 1110,1111)
From the List 1 or first List table as shown below:
LIST 1
Index Dec A B C D
Group 1 1 1 0 0 0 1
8 1 0 0 0
3 0 0 1 1
5 0 1 0 1
Group 2 2 9 1 0 0 1
10 1 0 1 0
12 1 1 0 0
7 0 1 1 1
11 1 0 1 1
Group 3 3 13 1 1 0 1
14 1 1 1 0
Group 4 4 15 1 1 1 1
From List 2 by combining the groups, group 1 with group 2, group 2 with group 3 and group 3 with
group 4. Groups are not allowed to overlap, for example group 0ne cannot be combined with group 3.
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