Determine reduced boolean equation and the karnaugh map, Computer Engineering

Assignment Help:

Determine reduced Boolean equation and the Karnaugh Map?

Illustration: Determine reduced Boolean equation and the Karnaugh Map for the truth table shown below:

C

A

OUTPUT

0

0

1

0

1

1

0

0

1

0

1

1

1

0

1

1

1

0

1

0

0

1

1

0

With no reduction the Boolean Equation for the above truth table is:

Y = A'B'C' + AB'C' + A'BC' + ABC' + A'B'C

Every minterm corresponds to an instance in the truth table when the output is high and the Karnaugh Map for the above truth table, with the allowed groupings is shown below:

1068_Determine reduced Boolean equation and the Karnaugh Map.png

The map shows two groupings that cover every minterm each of these groupings will reduce to one term.

The two terms those are grouped together A'B'C & A'B'C' reduces to A'B' this is because A' and B' are common to both terms.

The four terms A'B'C' & A'BC' & ABC' & AB'C' that is grouped together reduces to C' this is because C' is the only input common to all four terms.
Thus the Boolean equation Y = A'B'C + A'B'C' + A'BC' + ABC' + AB'C' reduces to

Y = A'B' + C'.


Related Discussions:- Determine reduced boolean equation and the karnaugh map

Drawback of the system using disk caching, Q. Drawback of the system using ...

Q. Drawback of the system using disk caching? The main drawback of the system using disk caching is risking loss of updated information in event of machine failures like loss o

Constraint satisfaction problems, Constraint Satisfaction Problems: Fu...

Constraint Satisfaction Problems: Furthermore I was perhaps most proud of AI on a Sunday. However this particular Sunday, a friend of mine found an article in the Observer reg

Explain the microprocessor development system, Microprocessor development s...

Microprocessor development system Computer systems have undergone many changes recently. Machines that once filled large areas have been reduced to small desktop computer syste

Explain clearly the difference between j-cuts and l-cuts, Question: (a)...

Question: (a) Explain clearly the difference between J-cuts and L-Cuts. (b) What is the function of the rate stretch tool? (c) What's the difference between an Image Matt

Exit command, Your shell must accept the exit command. This command will ...

Your shell must accept the exit command. This command will be in the form: e x i t When you encounter this command, your shell should terminate. Please note that when you

Can you explain about internet protocol, Q. Can you explain about Internet ...

Q. Can you explain about Internet Protocol? Internet protocol specifies the rules which define the details of how computers communicate. It specifies exactly how a packet shoul

What is microcomputer system, Q. What is microcomputer system? The micr...

Q. What is microcomputer system? The microcomputer has a single microprocessor and a number of RAM and ROM chips as well as an interface unit which communicates with several ex

Perceptrons of artificial neural networks, Perceptrons: However the we...

Perceptrons: However the weights in any ANN are usually just real numbers and the learning problem boils down to choosing the best value for each weight in the network. Becaus

Explain the terms topology used in lans, Explain the terms topology used in...

Explain the terms topology used in LANs. (i) LAN topologies: This network topology is a physical schematic that shows interconnection of the several users. There are four fun

Convert binary number in two''s compliment form, Convert binary number in t...

Convert binary number in two's compliment form 0100 1000. Converting the binary number into 2's compliment from 0100 1000 is given below: 01001000 => 10111000

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