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

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

Computer peripherals, Describe the 8251 A programmable communication interf...

Describe the 8251 A programmable communication interface

What is gimps native graphics file format, XCF is GIMP's "native" format. T...

XCF is GIMP's "native" format. This will preserve all information about an image, having the layers.

Mating - canonical genetic algorithm, Mating: Therefore once our GA ag...

Mating: Therefore once our GA agent has chosen the individuals lucky sufficient as actually there  fit enough to produce offspring then we next determine how they are going to

Device drivers in ms-dos, In MS-DOS device drivers are installed and loaded...

In MS-DOS device drivers are installed and loaded dynamically it implies that they are loaded into memory when computer is started or re-booted and accessed by operating system as

Define memory management system, Define memory management system? The p...

Define memory management system? The part of the computer system that supervises the flow of information among auxiliary memory and main memory is known as memory management sy

Illustrate the table of types of serach engines, Illustrate the table of ty...

Illustrate the table of types of serach engines Type in: CIE and the search engine would return about 22 million hits Type in

Does average velocity differ from its instantaneous velocity, Q. When an ob...

Q. When an object travels with constant velocity does its average velocity during any time interval differ from its instantaneous velocity at any instant? Answer:- No It i

Example of a router connects to at most networks, A router connects to at m...

A router connects to at most K networks. How many routers R are required to connect to N networks? Derive an equation that gives R in terms of N and K. If N K and K >=2 this

Why process scheduling algorithm favour i/o bound processes, Suppose that a...

Suppose that a process scheduling algorithm favors those processes that have used the least processor time in the recent past. Why will this algorithm favour I/O- bound processes,

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