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

Draw layout cells in a table, Now add layout cells into which you will add ...

Now add layout cells into which you will add text about travel locations. 1.  In Objects panel, click the Draw Layout Cell icon and move the pointer to layout table you just dre

Interrupt and scanning method of keypad operation, INTERRUPT METHOD - USING...

INTERRUPT METHOD - USING PORTB CHANGE INTERRUPT By using 4 by 4 matrix keypad connected to PORTA and PORTB. The rows are connected to PORTA-Low (RA1-RA4) and the columns are co

Explain the biometric systems and biometric authentication, Explain the Bio...

Explain the Biometric Systems in brief. Biometrics: It is the science of measuring physical properties of living beings. Biometric Authentication: (a) This authenticati

#title., REPRESENTATION OF POYNOMIAL OF 2 OR MORE VARIABLES USING ARRAY

REPRESENTATION OF POYNOMIAL OF 2 OR MORE VARIABLES USING ARRAY

Superscalar processors, Superscalar Processors In scalar processors, on...

Superscalar Processors In scalar processors, only one instruction is implemented per cycle. That means only single instruction is issued per cycle and only single instruction i

Queue, A Queue is a FIFO ( rst in, rst out) data structure. Given the foll...

A Queue is a FIFO ( rst in, rst out) data structure. Given the following queue interface: public interface Queue { int size(); // current queue size boolean isEmpty(); //

What is the use of status command, What is the use of status command, data ...

What is the use of status command, data output command, and data input command. A status command is used to test a variety of status conditions in the interface and the periphe

what respects the advance builds, Describe your choice specifically and fu...

Describe your choice specifically and fully, explaining and discussing at length in what respects the advance builds upon or departs from present technology or practice and the sev

Performance analysis, In order to calculate the performance of the program,...

In order to calculate the performance of the program, the normal form of analysis of the program is to simply measure the total amount of CPU time needed to implement the various p

Graph has a minimum spanning tree already computed, Assume that a graph has...

Assume that a graph has a minimum spanning tree already computed.  How fastly can the minimum spanning tree be updated if a new vertex and incident edges are added to G? If the

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