Boolean Algebra and Logic Gate

INTRODUCTION

In this chapter, we will look at Boolean algebra, truth table, basic and combinational logic. It is all because in the CPU, we have discussed about the ALU, registers,multiplexer and etc as abstract object. Any of these following terms or variables and logic may gives impact to the development of the system and give a better to work with the logic.

3.1 Boolean Algebra

l  In Boolean Algebra,

Ø  uses variables and operators to describe logic circuits

Ø  allows all the variables and operators to have only one possible values, 0 and 1.

Ø  the complement of a variable is shown by a bar over the letter. For example,

given variable A is 1, the complement A of the variable is 0

3.2 LAW OF BOOLEAN ALGEBRA

•   Boolean expressions can be simplified or  multiplied
• The basic law of BOOLEAN  ALGEBRA
  
  
  
  Identity Law:
  
  

  AND form	OR form
  ²  A.1 = A	²    A + 0 = A

  
  
   Zero and One Law:
  
  

  AND form	OR form
  ²  A.0 = 0	²  A + 1 = 1

  
  
  Inverse Law:

  AND form	OR form
  ²  A.A’ = 0	²  A + A’ = 1

     Idempotent Law:

AND form	OR form
²  A.A=A	²  A+A = A

 Commutative Law:

AND form	OR form
²  A.B = B . A	²  A + B = B + A

Figure 3.1: Commutative law for AND form and OR form

Associative Law:

AND form	OR form
²  A.(B.C) = (A.B ).C	²  A+(B+C)=(A+B)+C

AND form

OR form

²  A.(B.C) = (A.B ).C

²  A+(B+C)=(A+B)+C

Figure 3.2 Associative Law for AND form and OR form

Distributive Law:

AND form	OR form
²  A+(B.C)=(A+B).(A+C)	²  A.(B+C)=(A.B)+(A.C)

Absorption Law:

AND form	OR form
ü  A(A+B)=A	ü  A+A.B=A ü  A+A’.B=A+B

AND form

OR form

²  A+(B.C)=(A+B).(A+C)

²  A.(B+C)=(A.B)+(A.C)

AND form

OR form

ü  A(A+B)=A

ü  A+A.B=A

ü  A+A’.B=A+B

EXAMPLE :

Demorgan’s  Law

Written by:

Name: Chiang Han Sheng,Lim Chi Hong
No. matrik: B031210078,B031210028