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

Show how pages will be allocated using first-in-first-out, Consider the fol...

Consider the following page reference and reference time strings for a program: Page reference string: 5,4,3,2,1,4,3,5,4,3,2,1,5,..... Show how pages will be allocated using t

What is macro call, What is macro call? Explain. Macro call: While a...

What is macro call? Explain. Macro call: While a macro name is used along with a set of actual parameters this is replaced through a code generated from its body. Such code

Illustrate the logical view of a system, Illustrate the Logical view of a s...

Illustrate the Logical view of a system The Logical view of a system serves to describe existence and meaning of key abstractions and mechanism which form problem space, or wh

What is the gray equivalent of decimal number 25, What is the Gray equivale...

What is the Gray equivalent of  (25) 10 Ans. Gray equivalent of (25) 10 : The Decimal number 25 has binary equivalent as (00100101) 2 The left most bits (MSB) into gray

CPE, WHAT IS CPE

WHAT IS CPE

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

Explain system software with system programming, Explain the evolution of s...

Explain the evolution of system software with system programming. System-software is collection of system programs which perform a variety of functions, name are: file editing,

What is memory mapped i/o, What is memory mapped I/O? When the I/O devi...

What is memory mapped I/O? When the I/O devices share the similar address space, the arrangement is known as memory mapped I/O.

Explain the programmable rom (prom) - computer memory, Explain the Programm...

Explain the Programmable ROM (PROM) - Computer Memory? This is a kind of ROM that can be programmed using special equipment it can be written to, but only once and this is usef

Explain data rates in public switched telephone network, Explain data rates...

Explain data rates in public switched telephone network. Data rates in PSTNs : A voice channel in a public switched telephone network is band restricted with a nominal bandwid

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