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

Explain about the various uses of artificial intelligence, Discuss the use ...

Discuss the use of Artificial intelligence techniques in E-Commerce applications. Explain about the various uses of Artificial Intelligence in Medicine field. Justify it with pr

What is program annotation packages, Q. What is Program Annotation Packages...

Q. What is Program Annotation Packages? A quite renowned scheme in this field is OpenMP a newly designed industry standard for shared memory programming on architectures with u

Algorithm, i need algorithm for padovan string

i need algorithm for padovan string

Database management system, what is time out based schemes in concurrency c...

what is time out based schemes in concurrency control

.bus, clasification of bus

clasification of bus

How to join to mwseries from power builder 8.0, Using CICS Transaction Gate...

Using CICS Transaction Gateway we can join MQ Series with Power Builder 8.0

Determine the list of micro-operations, Micro-Operations A micro-operat...

Micro-Operations A micro-operation is an basic operation which is performed on data stored in registers. We can classify micro-operations into four categories: 1. Register t

Transfer of control, Question a) Name and explian the four essential ...

Question a) Name and explian the four essential elements of a machine instruction. b) Provide any four common examples of mnemonics. c) The level of disagreement conce

Illustrate about the three state table buffers, Three state table buffers ...

Three state table buffers Three state table buffers: A bus system can be constructed with the help of three state gates instead of multiplexers. A three states gate is digital

Which of the memory is volatile memory, Which of the memory is volatile mem...

Which of the memory is volatile memory ? Ans. A volatile memory is RAM. Term Volatile memory implies the contents of the RAM get erased as soon as the power goes off.

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