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

How the characters used in operand data type, Q. How the Characters used in...

Q. How the Characters used in operand data type? A common form of data is character or text strings. Characters are signified in numeric form mostly in ASCII (American Standard

How aliases are used in DNS, How aliases are used in DNS? Explain. CNAM...

How aliases are used in DNS? Explain. CNAME entries are analogous to a symbolic link in a file system- the entry gives an alias for other DNS entry. Corporation of expertsmind

Illustration of display on video monitor, Q. Illustration of Display on Vid...

Q. Illustration of Display on Video Monitor? Displaying a single character ; display contents of BL register (Presume that it has a single character) MOV AH, 02H MOV D

Environments -artificial intelligence, Environments: We have seen that...

Environments: We have seen that an agents intelligent should take into account certain information when it choose a rational action, including information from its sensors, in

Why is c standard library needed, Why is C standard library needed?  C ...

Why is C standard library needed?  C Standard Library: C would have been a tough programming language in absence of the standard library. The standard library in C contains

Sms gateway application, The most important in the project are to develop a...

The most important in the project are to develop application: 1- Web Conference this will help both the jobseeker and employer to meet through web conference and follow the proc

Network throughput-network properties, Network throughput It is an indi...

Network throughput It is an indicative measure of the point carrying capacity of a network. It is distinct as the total number of messages the network can transmit per unit tim

What are condition code flags, What are condition code flags? The proce...

What are condition code flags? The processor keeps track of information about the results of several operations for use by subsequent conditional branch instructions. This is a

Explain about the mini computers, Explain about the MINI COMPUTER Minic...

Explain about the MINI COMPUTER Minicomputers are much smaller in size than mainframe computers and they are also less expensive.  The cost of these computers can differ from a

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