Page 32 - Handout Digital Electronics

LECTURER 4 COMBINATIONAL LOGIC CIRCUITS

4.1. Boolean algebra
Boolean algebra is the most fundamental tool used to analyze and describe the operations of digital
logic circuits. Digital computers are built on digital logic circuits and the digital logic circuits are derived
from Boolean functions /expressions.

The obvious way to look at Boolean functions is to manipulate them in the same way as
conventional/normal algebraic expressions but one must stick to the set of rules formulated by the
English Mathematician George Boole.

In Boolean algebra, a variable says A can take only two valuations, i.e. A = 1 or 0, which have also the
logic interpretations True for A = 1 and False for A= 0 or High for A=1 and Low for A = 0, and On for A =
1 and Off for A = 0. A = 0 is also known as A (NOT A).

The basic Boolean operators are:

• AND (∙)
• OR (+)
• NOT (-)

Boolean equations/expressions are formed by combining Boolean variables with Boolean operators for
example: F A.B B(C D) . The application A.B can be written simply as AB. When Boolean variables
are combined with Boolean operators several rules can be derived from these relations. These basic
rules are called postulates or rules of Boolean algebra. Postulates are basic axioms that are rules that
have proven beyond any reasonable doubt that they are correct, so they do not need any proof.

Examples of Postulates

P1: A = 0 or A = 1

P2: 0.0 = 0

P3: 1+0 = 1

P4: 0+0 = 0

P5: 1.1= 1

P6: 1+1=1

P7: 1.0 = 0

These Boolean postulates are used to prove laws and theorems of Boolean algebra.

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