Determine Boolean identities using Boolean algebra, Computer Engineering

Assignment Help:

Prove the following identities
 
a. A
‾B‾C‾ + A‾BC‾ + AB‾C‾ + ABC‾ = C
b. AB + ABC + A
‾ B + AB‾C = B + AC

Ans.

a. LHS = A'B'C' + A'BC' + AB'C' + ABC'
= A'C' (B' + B) + AC' (B' + B)
= A'C' + AC'   [as B'+B = 1]
= C' (A' + A)
= C'                   [since A'+A =1]
= RHS.
Thus Proved

b. LHS = AB + ABC + A'B + AB'C

= B + AC
= B (A + A') +  AC (B + B')
= B + AC   [as B + B' = A + A' = 1]
= B + AC
= RHS.
Thus Proved


Related Discussions:- Determine Boolean identities using Boolean algebra

How will you allocate sub system, How will you allocate sub system? All...

How will you allocate sub system? Allocate every concurrent subsystem to hardware unit. General purpose processor or specialized functional unit as follows: Estimate per

Logical functions, Logical functions   We have discussed the If, 'While...

Logical functions   We have discussed the If, 'While and For' Statements, and have used expressions within our syntax i.e.           If ( expression)           Statement 1;

Write an awk program - unix , Write an AWK program which takes the followin...

Write an AWK program which takes the following input file and processes it. $cat data.txt John Do 111-1111 English 90 Maths 80 Alice Do 222-2222 English 90 Maths 90 Chemistry 93

Where arq is transmitted, ARQ is transmitted in the event of: (A)  Los...

ARQ is transmitted in the event of: (A)  Loss of signal                          (B) Error in received data (C)  Improve reliability                  (D) During time out

Show the comparison of ascii and ebcdic, Q. Show the Comparison of ASCII an...

Q. Show the Comparison of ASCII and EBCDIC? EBCDIC is an easier to employ code on punched cards due to BCD compatibility. But ASCII has some of major benefits on EBCDIC. These

What are the general security issues, What are the General Security Issues ...

What are the General Security Issues Many issues exist when linking a computer system to the Internet or indeed to an external link via a network set up. There are numerous way

How to copy files from a drive and directory, Q. How to copy files from a d...

Q. How to copy files from a drive and directory? You can copy files from a drive and directory other that the currently selected one. However in that case, you need to speci

Visualization, Visualization Visualization is a general method in contr...

Visualization Visualization is a general method in contract to search based tools.  In this method visual aids are given like pictures to assist the programmer in evaluating th

Avoiding overfitting - decision tree learning , Avoiding Overfitting : ...

Avoiding Overfitting : However remember there that in the previous lecture, there is over fitting that common problem in machine learning. Furthermore details to decision tree

Describing Random Algorithm, Suppose you''re given n numbers and asked to f...

Suppose you''re given n numbers and asked to find a number that is greater than or equal to the median a) What is the lower bound for the worst case complexity of this problem?

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