Page 63 - Handout Digital Electronics

1 4 1 0 0

Group 3 2 5 1 0 1

LIST 2

List two is formed by combining group 1 with group 2 and group 2 with group 3. Groups are not
allowed to overlap. After combining any two groups, horizontal line is used to separate the new group
from the next following group. New groups will be formed as a result. The new groups can still be
combined to remove some redundancies, for example, the new groups are 1 and 2.

Dec A B C

1) 0, 1 0 0 - ✓

0, 4 - 0 0 ✓

2) 1, 5 - 0 1 ✓

4, 5 1 0 - ✓

LIST 3

List 3 is formed in a similar way to list two, but in this list those minterms that have combined must be
identified by some mark and those that have not combined must be identified by a different symbol or
mark.

Dec A B C

0, 1, 4, 5 - 0 -

0, 4, 1, 5 - 0 -

From the results of list three, (3) the result cannot be reduced any further, so, minimized F = B is the
function.

Example 2

Minimize the Boolean function below using the tabular method: F (A, B, C) =∑ (0, 1, 2, 3, 4, 6)

Convert to binary notation:

F (A, B, C) =∑ (000, 001, 010, 011, 100, 110)

The conversion allows us to produce a list or table where minterms with the same index (no of binary
ones (1s) are put in respective groups. For example, 000 has zero ones so it will be in a group of its own.
001 and 010 have one binary each so they will be in the same group. The same applies to 011 and 101,
they each have two binary ones so they will be in the same group also.

See list 1 below

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