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

Describe about the desk top publishing, Desk Top Publishing (DTP) As wo...

Desk Top Publishing (DTP) As word processors develop increasingly more sophisticated features, differences with desk top publishing (DTP) packages becomes more and more blurred

Reduce minimum literals and derive their complements, Q. Reduce following t...

Q. Reduce following to minimum literals and derive their complements. 1. [(AB)'A][(AB)'B] 2. ABC(ABC' + AB'C + A'BC) 3. (A+C+D) (A+C+D') (A+C'+D)(A+D')

What are the advantages of using xml over html, What are the advantages of ...

What are the advantages of using XML over HTML? The root cause of the problem lies within HTML that is Hyper Text Markup Language, the defector standard for web publication. Th

Concept of temporal parallelism, Concept of Temporal Parallelism In ord...

Concept of Temporal Parallelism In order to describe what is meant by parallelism inherent in the answer of a problem, let us talk about an example of submission of electricity

Use string manipulating functions , Write a script that will first initiali...

Write a script that will first initialize a string variable that will kept x and y coordinates of a point in the form 'x 3.1 y 6.4'.  Then, use string manipulating functions to ext

Create a sliding puzzle, As demonstrated in a simple manner in my Animated ...

As demonstrated in a simple manner in my Animated Tiles example, the purpose of this assignment is to use jQuery animations to develop a simple puzzle using DIV tags and styles. C

The long and short date option , In MS Access, the long and short date opti...

In MS Access, the long and short date option does not show 4 digit years. How do I achieve the mm/dd/yyyy format? Ans) In the date field properties of the table, form, or prop

How many types of stages include in process of data mining, How many types ...

How many types of stages include in process of data mining? The process of data mining comprised three stages as given below: a) The initial exploration b) Model buildin

C++, pebble merchant

pebble merchant

what is lrd_stmt?, The lrd_stmt function associates a character string (ge...

The lrd_stmt function associates a character string (generally a SQL statement) with a cursor. This function sets a SQL statement to be processed.

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