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 integrated disk electronics devices, Q. Explain Integrated Disk Ele...

Q. Explain Integrated Disk Electronics Devices? IDE devices are associated to PC motherboard by a 34-wire ribbon cable. Common drive used today for workstations has capacities

By which companding helps in reducing signal, Companding helps in reducing ...

Companding helps in reducing with respect to signal:  (A) Interference                    (B) Signal overloading (C) Non linearity                 (D) Quantization noise

Explain abstract class, What is an interface and what is an abstract class?...

What is an interface and what is an abstract class? Please, expand by examples of using both. Explain why?   Abstract classes are closely related to interfaces. They are classe

Data transmission and modems, Q. What is Data Transmission and Modems? ...

Q. What is Data Transmission and Modems? Data can be transferred between two stations in either serial or parallel transmission. Parallel data transmission, in which a group of

Transport layer, time to left (TTL) in transport layer

time to left (TTL) in transport layer

Explain what are user controls, Briefly explain what user controls are and ...

Briefly explain what user controls are and what server controls are and the differences between the two.   An ASP.NET control (sometimes known as a server control) is a server-

Explian service topologies, Explian Service Topologies Service Topolog...

Explian Service Topologies Service Topologies In a service-based architecture there increase dependencies between services resulting from cooperation

Examples of artificial neural networks, Examples of artificial neural netwo...

Examples of artificial neural networks: Now here as an example consider a ANN that has been trained to learn the following rule categorising the brightness of 2x2 black and wh

What happens if acknowledge() is called within a transaction, As per the JM...

As per the JMS specification, when you are in a transaction, the acknowledge Mode is ignored. If acknowledge() is known as within a transaction, it is ignored.

Quick sort exhibit its worst-case behaviour, In which input data does the a...

In which input data does the algorithm quick sort exhibit its worst-case Behaviour? The Quick Sort method exhibits its worst-case behavior when the input data is " Already Comp

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