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

Define optimistic synchronization, Q. Define Optimistic Synchronization? ...

Q. Define Optimistic Synchronization? Optimistic Synchronization: This method too updates atom by requester process however sole access is granted after atomic operation by abo

Pruning and sorting, Pruning and Sorting: This means we can test where...

Pruning and Sorting: This means we can test where each hypothesis explains as entails a common example that we can associate to a hypothesis a set of positive elements in whic

Write an algorithm for deadlock detection, Write an algorithm for deadlock ...

Write an algorithm for deadlock detection. An algorithm for deadlock detection: 1. Assume that Work and Finish be vectors of length m and n, correspondingly. Initialize:

Convert logic circuit in a binary code, The logic circuit given below, conv...

The logic circuit given below, converts a binary code y 1 y 2 y 3 into Ans. Gray code is X1 = Y1,   X2 = Y1 XOR Y2  ,   X3 = Y1 XOR Y2 XOR Y3 For

Integrating virtual memory, Integrating Virtual Memory, TLBs, and Caches - ...

Integrating Virtual Memory, TLBs, and Caches - computer architecture:   There are 3 types of misses: 1. a cache miss 2. TLB miss 3. a page fault 2 techniqu

Show arithmetic subtraction, Q. Show Arithmetic Subtraction? The subtra...

Q. Show Arithmetic Subtraction? The subtraction can be done easily using 2's complement by taking 2's complement of value which is to be subtracted (inclusive of sign bit) and

Define the system analysis of object oriented modelling, Define the System ...

Define the System Analysis of Object oriented modelling System Analysis: In this stage a statement of the queries is formulated and a model is designed by the analyst in enc

Explain about working of multiplexer, Q. Explain about working of Multiplex...

Q. Explain about working of Multiplexer? Multiplexer is one of the fundamental building units of a computer system that in principle permits sharing of a common line by more th

Explain the pdca cycle, Explain the PDCA cycle. PDCA is a four step pro...

Explain the PDCA cycle. PDCA is a four step problem solving method. The following are the description of each step: 1. P - Plan (Devise your Plan). Identify an opportunity a

How can one decide this decimal position, Q. How can one decide this decima...

Q. How can one decide this decimal position? Decimal position can be signified by a position between flip-flops (storage cells in computer). However how can one decide this dec

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