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

Describe about digital audio tape, Q. Describe about Digital Audio Tape? ...

Q. Describe about Digital Audio Tape? The most proper tape for backing up data from a disk today is Digital Audio Tape (DAT). It employs a 4mm tape covered in a cartridge. It e

What are interrupts, What are interrupts?  Interrupt: An interrupt i...

What are interrupts?  Interrupt: An interrupt is a hardware mechanism which enables an external device, classically input/output devices, to send a signal to the CPU. An int

What are the advantages of using uml, Benefits of using UML breaks the comp...

Benefits of using UML breaks the complex system into discrete pieces that can be understood simply. Handover the system to new team becomes simpler. Complex system can be un

Drawing sequential circuit on paper, design a sequential circuit that conti...

design a sequential circuit that continuously computes the function 2X + 3 or 3X + 1 where the variable X is a three-bit unsigned integer available on a serial interface. A special

How many bits of data will be produced if voice is converted, If voice is c...

If voice is converted to digital form using PCM, how many bits of data will be produced in half a second? While voice is converted to digital by using PCM that is Pulse Code Mo

Modified digital clock, can you deign the schematic of a modified digital c...

can you deign the schematic of a modified digital clock at the gate as well as the IC level and then construct the circuit, lab spec and industral spec?

A* search - artificial intelligence, A* Search - artificial intelligence: ...

A* Search - artificial intelligence: A* search in the combines is the best parts of uniform cost search, namely the fact that it's optimal and complete, and the other best par

ERP, Benefits of implementing ERP

Benefits of implementing ERP

Define side tone is essential in telephone communication, A certain amount ...

A certain amount of side tone is essential in telephone communication. Ans: It is true that a specific amount of side tone is necessary in telephone communication.

Find the generating function, Find the generating function to denote the nu...

Find the generating function to denote the number of ways the sum 9 can be acquired while 2 distinguishable fair dice are tossed and the first shows an even number and the second s

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