Dld lecture module 05

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Digital Logic & Design
Dr. Sajjad Ahmed Nadeem
Department of Computer Science & IT
University of Azad Jammu & Kashmir
Muzaffarabad
Module 04
Basic Definitions
Postulates.
Principle of duality.
Theorems.
Proving a Theorem.
Algebraic Expressions.
TruthTable.
Minimization.
Complement.

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Basic Definitions
Binary Operator
A binary operator defined on a set S of
elements is a rule that assigns, to each pair of
elements from S, a unique element from S.
Boolean Algebra
Boolean algebra is an algebraic structure
defined by a set of elements, B, together with
two binary operators, + and ., provided that the
postulates of Boolean algebra are satisfied.
Postulates of Boolean Algebra

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Postulates of Boolean Algebra
The Principle of Duality

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ImportantTheorems of Boolean
Algebra
Methods of Proving Theorems

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Proving a Theorem by using Postulates
andTheorems
[ x.1 = x ]
[ x.(y+z)=(x.y) + (x.z) ]
[ x+y=y+x ]
[ x+1=1 ]
[ x.1=x ]
Proving a Theorem by Perfect
Induction / Exhaustive Enumeration
[x + x.y = x ]

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Proving a Theorem by Duality
[ x.1=x ]
[ x +x=1 ]
[ x+(y.z)=(x+y).(x+z) ]
[x.x=0 ]
[ x+0=x ]
[ x+0=x ]
[ x . x=0 ]
[ x.(y+z)=(x.y)+(x.z) ]
[ x+x=1 ]
[ x.1=x ]
Reading Assignment:Venn Diagrams

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Boolean Functions
Representation of a Boolean
Function as an Algebraic Expression

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Representation as a TruthTable
Representation as a TruthTable

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Manipulations/Minimizations of
Boolean Functions
Manipulations/Minimizations of
Boolean Functions

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Try out some minimization!
Complement of a Boolean Function

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Complement of a Boolean Function