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

Illustration of equivalent exe program, Q. Illustration of equivalent EXE p...

Q. Illustration of equivalent EXE program? An illustration of equivalent EXE program for COM program is: ; ABSTRACT this program adds 2 8-bit numbers in the memory locations

What are the advantages of using uml, Benefits of using UML breaks the comp...

Benefits of using UML breaks the complex system into discrete pieces that can be understood simply. Handover the system to new team becomes simpler. Complex system can be un

Dataflow computing, Dataflow Computing A different to the von Neumann m...

Dataflow Computing A different to the von Neumann model of computation is the dataflow computation model. In a dataflow model, control is fixed to the flow of data. The order o

Priority array, The runqueue is the list of runnable processes on a given p...

The runqueue is the list of runnable processes on a given processor. There is only one runqueue per processor. Each runqueue contains two priority arrays: Active and Expired. Each

How can you show only selected records with a form, How can you show only s...

How can you show only selected records with a form? There are dissimilar ways in which you can limit the records that you will see with a form, you can: Open a form and app

What is event-driven control, What is event-driven control? Control res...

What is event-driven control? Control resides within a dispatcher or monitors that language, subsystem or OS provider. Developers attach application process to events and dispa

What is database integration, What is database integration? Database in...

What is database integration? Database integration is the ability to give user-friendly and cost-effective software solutions for data infrastructure management by the interfac

Need of the assembly language, Q. Need of the assembly language ? Machi...

Q. Need of the assembly language ? Machine language code comprises the 0-1 combinations which computer decodes directly.  Though the machine language has the following problems

What are instruction hazards, What are instruction hazards? The pipelin...

What are instruction hazards? The pipeline might also be stalled because of a delay in the availability of an instruction. For instance, this may be a result of a miss in the c

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