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

Object oriented systems analysis and design, Analysis and design form the b...

Analysis and design form the basis on any significant software artifact. Analysis is critical in terms of making sure that the final artifact actually meets user requirements (ie b

Implementing protection with virtual memory, Implementing Protection with V...

Implementing Protection with Virtual Memory - computer architecture: To enable the operating system to implement protection in the VM system, the HW have to: I. Support at

Connectives in first-order logic sentences, Connectives in first-order logi...

Connectives in first-order logic sentences - Artificial intelligence We may string predicates together into a sentence in the same way by utilising connectives that we did for

What are the data types of vhdl, What are the Data types of VHDL VHDL....

What are the Data types of VHDL VHDL. A multitude of language or user defined data types can be used. This may mean dedicated conversion functions are needed to convert object

What is analysis and list its sub stages, What is analysis, list its sub st...

What is analysis, list its sub stages? Understand the requirement by constructing models. The goal of analysis is to state what need is to be done and not how it is to be done.

arithmetic pipelines, Arithmetic Pipelines The method of pipelining ca...

Arithmetic Pipelines The method of pipelining can be applied to a variety of complex and slow arithmetic operations to speed up the processing time. The pipelines used for arit

Input output techniques - computer architecture, Input Output Techniques: ...

Input Output Techniques: o   Interrupt driven o   Direct Memory Access (DMA) o   Programmed Programmed I/O   CPU has control over I/O directly   Read/write

Why the tcp checksum is necessary, Is the TCP checksum necessary? Yes, ...

Is the TCP checksum necessary? Yes, TCP Checksum is essential. TCP layer is liable for error detection, transmission of packets if needed, error control, reassembly of packe

Acting rationally - artificial intelligence, Acting Rationally: "Al" C...

Acting Rationally: "Al" Capone was finally convicted for tax evasion. Were the police reacting on rationally?? To solve this puzzle, we must first look at how the performance

Explain file transfer protocol, Explain File Transfer Protocol . FTP is ...

Explain File Transfer Protocol . FTP is utilized to exchange files among computer accounts, to transfer files among an account and a desktop computer (upload) or to access softw

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