Page 70 - Handout Digital Electronics

5, 7 0 1 - 1✓

5, 13 - 1 0 1✓

12, 13 1 1 0 -

7, 15 - 1 1 1✓

13, 15 1 1 - 1✓

The minterms marked with the asteristic () have not combined with any minterms and should be part
of the final answer

LIST 3

Dec A B C D

0, 1, 2, 3 0 0 - -

0, 2 ,1 ,3 0 0 - -

0, 2, 8, 10 - 0 - 0

0, 8, 2, 10 - 0 - 0

1, 3, 5, 7 0 - - 1
1, 5, 3, 7 0 - - 1

5, 7, 13, 15 - 1 - 1

5, 13, 7, 15 - 1 - 1

The prime implications florists’ 3 and 4 are:

F = AB + BC + AD + BD + ACD + ABC

The prime implicates ACD, ABC are from list 2 and are marked with an asterisk to show that they have
not combined with any other minterm. This means that they should be included in the final list of prime
implications.

Rule 2

Any minterm(s) that has not combined with any other, starting from list 2 onwards must be part of the
final function.

A look at the Boolean expression: F = AB + BC + AD + BD + ACD + ABC shows that there are
redundant implications. These can be reduced by using a chart.

The chart is a grid made up of implicates listed at the left and all the minterms of the function along the
top. This means the implicants represent the rows and the minterms the columns. Each minterm
represented by a given implicate is marked in the appropriate position (see diagram below):

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