Define minterm and the maxterm - canonical form, Computer Engineering

Assignment Help:

Define Minterm and the Maxterm - Canonical Form?

Any Boolean expression perhaps expressed in terms of either minterms or maxterms. The literal is a single variable within a term which may or may not be complemented. For an expression with the N variables, minterms and maxterms are defined as follows:

A minterm is the product of the N distinct literals where each literal occurs exactly once.

A maxterm is the sum of the N distinct literals where each literal occurs exactly once.

For the two-variable expression, the maxterms and minterms are as follows

X

Y

Minterm

Maxterm

0

0

X'.Y'

X+Y

0

1

X'.Y

X+Y'

1

0

X.Y'

X'+Y

1

1

X.Y

X'+Y'

For a three-variable expression, the maxterms and minterms are as follows

X

Y

Z

Minterm

Designation

Maxterm

Designtion

0

0

0

X'.Y'.Z'

m0

X+Y+Z

M0

0

0

1

X'.Y'.Z

m1

X+Y+Z'

M1

0

1

0

X'.Y.Z'

m2

X+Y'+Z

M2

0

1

1

X'.Y.Z

m3

X+Y'+Z'

M3

1

0

0

X.Y'.Z'

m4

X'+Y+Z

M4

1

0

1

X.Y'.Z

m5

X'+Y+Z'

M5

1

1

0

X.Y.Z'

m6

X'+Y'+Z

M6

1

1

1

X.Y.Z

m7

X'+Y'+Z'

M7

 Consider a function F= x'y'z+xy'z'+xyz=m1+m4+m7

If we take the complement of F then F'= (x+y+z')(x'+y+z)(x'+y'+z')=M1.M4.M7

Any Boolean function can be expressed as a product of Maxterms and Sum of Minterms.


Related Discussions:- Define minterm and the maxterm - canonical form

Specifying constraint problems, Specifying Constraint Problems: Howeve...

Specifying Constraint Problems: However as with most successful "AI" techniques there constraint solving is all about solving problems as: somehow phrase the intelligent task

show bank type , Describe an abstract class 'Bank' having abstract methods...

Describe an abstract class 'Bank' having abstract methods as 'CreateAccount' 'depositAmount' & 'withDrawAmount'.Add method definitions for 'CalculateInterest' and 'SetInterest' as

By using what nested macro calls are expanded, Nested Macro calls are expan...

Nested Macro calls are expanded using the? Ans. By using the LIFO (Last in First out) Nested Macro calls are expanded.

How is basic authentication worked, How is basic authentication worked? ...

How is basic authentication worked? When an exact resource has been protected using fundamental authentication, Apache sends a 401 Authentication needed header along with the r

Recombination - canonical genetic algorithm, Recombination: Therefore...

Recombination: Therefore during the selection and mating process then the GA repeatedly lines up pairs of individuals for reproduction. Hence the next question is how to gener

Compute the coefficient for classifier, Consider the data with categorical ...

Consider the data with categorical predictor x 1 = { green or red } and numerical predictor x 2 and the class variable y shown in the following table. The weights for a round

Illustrate abstract class, What is an abstract class? Please, expand by exa...

What is an abstract class? Please, expand by examples of using both. Explain why?   Abstract classes are closely related to interfaces. They are classes that cannot be instanti

Explain how the different access methods work, Question: (a) Primary an...

Question: (a) Primary and secondary memory differs in their way they access data: (i) Mention the four generic access methods usually present in a computer system. (ii) E

Define the concept of inheritance, Define the concept of Inheritance I...

Define the concept of Inheritance Inheritance is property of reusing the code within the object oriented development. While modelling, we look at the all the classes, and try

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd