Simplify the expressions using boolean postulates, Computer Engineering

Assignment Help:

Simplify the given expressions using Boolean postulates

XY + X‾Z‾  + XY‾Z (XY + Z)

Ans. XY + X‾Z‾ + XY‾Z (XY + Z)
= XY + X‾Z‾ + XY‾Z (XY + Z)
= XY + X‾Z‾  + XXYY‾Z + XY‾ZZ
= XY + X‾Z‾  + XYZ             (As YY‾ = 0 and ZZ = Z)
= XY + X‾ + Z‾ + XY‾Z (As X‾Z‾ = X‾ + Z‾)
= X‾ + XY + Z‾ + XY‾Z
= X‾ + X (Y + Y‾Z) + Z‾
= X‾  + X (Y +Z) + Z‾  (As Y + Y‾Z = Y+Z)
= X‾ + X Y (Z+ Z‾ ) + XZ + Z‾  (As Z+ Z‾  =1)
= X‾ + X Y Z + XYZ‾ + XZ + Z‾
= X‾ + XZ (1+ Y) + Z‾ (1+XY)
= X‾ + XZ + Z‾  (As 1+ Y = 1  and 1+XY = 1)
= X‾ + XZ) + Z‾
=(X‾ + Z) + Z‾  (As X‾ + XZ = X‾  + Z‾
= X‾  +( Z + Z‾)
= X‾ +1 (As Z + Z‾  = 1)
=1 (As X‾ +1 = 1)

 


Related Discussions:- Simplify the expressions using boolean postulates

What is jmx architecture, JMX is based on a 3-level architecture:   ?...

JMX is based on a 3-level architecture:   ? The Probe level have the probes (known as MBeans) instrumenting the resources. Also known as the Instrumentation level. ? The A

Explain pure and impure interpreters, Explain Pure and impure interpreters ...

Explain Pure and impure interpreters In a pure interpreter, the source program is retained into the source form all throughout its interpretation. These arrangements incur subs

How many and gates are required to realize Y = CD+EF+G, How many AND gates ...

How many AND gates are required to realize Y = CD+EF+G ? Ans. Y = CD + EF + G for realize this two AND gates are needed (for CD and EF).

What is reduction, What is reduction?  A reduction is a way of changing...

What is reduction?  A reduction is a way of changing one problem into another in such a way that a solution to the second problem can be used to explain the first problem.

create a class called auditorium, Create a class called auditorium that sp...

Create a class called auditorium that specifies the seats in the auditorium. The class should include at least one data item: seat (two dimensional array of Char) and at least thre

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

What is the conclude of the force of gravity on an object, Q. What is the...

Q. What is the conclude of the force of gravity on an object? Answer:- Force is the vector product of mass as well as acceleration F = ma. Weight is an unusual case of t

What is stack pointer, Stack pointer is a particular purpose 16-bit registe...

Stack pointer is a particular purpose 16-bit register in the Microprocessor, which grasp the address of the top of the stack.

Explain about interrupt servicing routines, Q. Explain about Interrupt serv...

Q. Explain about Interrupt servicing routines? First the situation is to be checked as to why the interrupt has happened. That includes not only device but also why the device

Differences between batch systems versus real-time systems, Question 1: ...

Question 1: a. Give NINE general properties of an MIS b. Name and explain the THREE main Problems and Issues of EIS Question 2: a. What are information systems for?

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