Post on 03-Mar-2017
6/14/2012
1
Digital Logic & Design
Dr. Sajjad Ahmed Nadeem
Department of Computer Science & IT University of Azad Jammu & Kashmir
Muzaffarabad
Module - 6
� Canonical and Standard Forms.
� SOP and POS.
� NAND and NOR Gates.
� Exclusive OR Function.
� Equivalence Function.
6/14/2012
2
Canonical and Standard Form
� Minterms For a boolean function of n variables , a product term in which each of the variables appears once (in either its complemented or uncomplemented form) is called a minterm.
� Maxterms For a boolean function of n variables , a sum term in which each of the variables appears once (in either its complemented or uncomplemented form) is called a maxterm.
Canonical and Standard Form
� Boolean functions expressed as a sum of minterms or product of maxterms are said to be in canonical form.
6/14/2012
3
Canonical and Standard Form
Minterms and Maxterms for three binary variables
6/14/2012
4
Sum of Products (SoP) Expression
Steps to express a Boolean Function in SOP Form
6/14/2012
5
Expressing a Boolean Function in SOP Form - Example
Expressing a Boolean Function in SOP Form - Example
6/14/2012
6
Product of Sums (PoS) Expression
Steps to express a Boolean Function in POS Form
6/14/2012
7
Expressing a Boolean Function in POS Form - Example
Expressing a Boolean Function in POS Form - Example
6/14/2012
8
Conversion between Canonical Forms (Sum of Products and Product of Sums)
NAND Gate
6/14/2012
9
NAND Gate
NOR Gate
6/14/2012
10
NOR Gate
Logic Gates
6/14/2012
11
Finding Booloean Expression of a Logic Circuit – Example 1
Finding Booloean Expression of a Logic Circuit – Example 1
6/14/2012
12
Finding Booloean Expression of a Logic Circuit – Example 2
Finding Booloean Expression of a Logic Circuit – Example 2
6/14/2012
13
Constructing a Logic Circuit from Boolean Expression – Example 1
Constructing a Logic Circuit from Boolean Expression – Example 1
6/14/2012
14
Constructing a Logic Circuit from Boolean Expression – Example 2
Constructing a Logic Circuit from Boolean Expression – Example 2
6/14/2012
15
Exclusive-OR Function
Exclusive-OR Function
6/14/2012
16
Equivalence Function
Equivalence Function