Page 31 - CITS - Electronic Mechanic - TT - 2024

ELECTRONICS MECHANIC - CITS

Laws of boolean algebra:
Complementation Laws
The term complements imply means to invert,i.e. to change 0’s to1’s and 1’s to 0’s.
Law 1:0’=1
Law 2: 1’=0
Commutative Laws:

Commutative laws allow change in position of AND or OR variables.
Law1:A+ B=B+ A
Proof:
This law can be extended to any numbers of variables fo re.g.

A+B +C= B+A+C= C+B+A=C+A+B

This law can be extended to any numbers of variables for e.g.
A·B· C=B · A·C= C·B·A= C·A·B
Associative Laws
The associative laws allow grouping of variables.
Law1: (A+ B)+ C=A+ (B+ C)
Proof:
This law can be extended to any no.of variables for e.g.
A+(B+ C+D) = (A+B +C) + D= (A+ B)+(C+D)

This law can be extended to any no.of variables for e.g.
A·(B· C · D) =(A·B ·C)·D= (A·B) ·(C·D)
Distributive Laws
The distributive laws allow factoring or multiplying out of expressions.

Law1:A (B+ C)= AB +AC
Proof:

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CITS : E & H - Electronics Mechanic - Lesson 5 - 8