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

Convert logic circuit to minimised, The logic circuit shown in the given fi...

The logic circuit shown in the given figure can be minimised to Ans. The minimised figure of logic diagram is D, the output of the logic circuit is as Y=(X+Y')'+(X'+(X+

Pervasive computing, Explain why pervasive computing can be termed as a “te...

Explain why pervasive computing can be termed as a “technology that disappears”

Explain the disadvantages off-the-shelf, Explain the disadvantages Off-the...

Explain the disadvantages Off-the-shelf -  can be over-complex since it tries to cover as many characteristics as possible (for example most users of Word only utilise about

BCD ADDER, create a BCD adder combinational ckt. that adds 2 digit BCD inpu...

create a BCD adder combinational ckt. that adds 2 digit BCD inputs

Internal structure of agents - artificial intelligence, Internal Structure ...

Internal Structure of Agents: We have looked at agents in terms of their external influences and behaviors: they put in from the surroundings and perform rational actions to a

Desirable choice for the partitioning element in quick sort, A desirable ch...

A desirable choice for the partitioning element in quick sort is First element of the list.

Explain the passive matrix in lcd technology, Q. Explain the Passive Matrix...

Q. Explain the Passive Matrix in lcd technology? In a passive matrix arrangement LCD panel has a grid of vertical and horizontal conductors and every pixel is positioned at an

Computer network architecture, A protocol is a formal description of messag...

A protocol is a formal description of message formats and the rules two or more machines must follow to exchange those messages. Because TCP (transmission control protocol) and IP

How future environment changes can be predicted - simulation, How future cl...

How future climate/environment changes can be predicted -  Information over time is fed into a weather/climate model -  based on changes in weather patterns, carries out a s

Register-to-register architecture, Register-to-Register Architecture : In t...

Register-to-Register Architecture : In this organization, results and operands are accessed not directly from the main memory by the scalar or vector registers. The vectors which a

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