Page 54 - Handout Digital Electronics
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7.2 Algebraic Method of Minimizing Boolean Expressions
The algebraic method makes use of the postulates/properties/laws of Boolean algebra as well as
theorems of Boolean algebra. For example, given the Boolean function below, minimize it using
postulates and theorems of Boolean algebra:
Example 1
F = AB + AB + AB
= A(B + B) + AB
= A + AB
= A + B
Example 2
F = ABC + ABC + ABC + ABC
= A(BC + BC ) + A(BC + BC)
= A(B C) + A(B C)
= A B C
Example 3
F = (A B AB)(A C AC) Minimize using the algebraic method
F = ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD
= ABD(C + C) + ABD(C + C) + ABD(C + C)
= ABD + ABD + ABD
= BD( A + A) + ABD
= BD + ABD = D(B + AB) = D(B + A) = D( A + B )
7.3 The Karnaugh Map Method of Minimizing Boolean Functions
The Karnaugh map provides a pictorial method of grouping together expressions with common factors.
It is a variation of the truth table, for example the two-variable truth table below can be represented in a
2- variable K map as shown below:
Table 1: A 2-variable truth table
A B F
0 0 a
0 1 b
1 0 c
1 1 d
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