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

Explain frame filtering, Write notes on Frame Filtering Techniques. Fr...

Write notes on Frame Filtering Techniques. Frame filtering: The most valuable function performed through bridges is frame filtering. A bridge doesn't forward a frame unles

What is called when network address prefixed by 1110, Network address prefi...

Network address prefixed by 1110 is a? Network address prefixed through 1110 is a multicast address.

State about the mainframe computer, Mainframe computer Mainframe comput...

Mainframe computer Mainframe computers are very large, often can fill an entire room. They can store a large amount of information, can execute many tasks at the same time, can

Cognitive science applications, This branch of AI is concerned with incor...

This branch of AI is concerned with incorporating knowledge from varied disciplines such as biolog neurology psychology mathematics and several linked disciplines. It is typic

What is shift operation, Q. What is Shift operation? Shift: Shift ope...

Q. What is Shift operation? Shift: Shift operation is employed for transfer of bits either to left or to right. It can be used to comprehend simple arithmetic operation or da

Origin of RISC, Q. Origin of RISC? In the 1980s a new philosophy develo...

Q. Origin of RISC? In the 1980s a new philosophy developed having optimizing compilers which could be used to compile 'normal' programming languages down to instructions which

IEEE802, 1. (a) Given a baseband bus with station 1 located at 10m, station...

1. (a) Given a baseband bus with station 1 located at 10m, station 2 located at 1000m, and station 3 located at 1010 meters (see diagram above). If the data rate of the bus is 10 M

What is fan-out, What is fan-out? Estimate the average count of every "...

What is fan-out? Estimate the average count of every "many" association encountered with the path. Multiply the individual fan-outs who obtain the fan-out of the whole path, wh

Cohesion and coupling, can i get a prepared ppt for this topic to present i...

can i get a prepared ppt for this topic to present it in a seminar??

How numbering plan is achieved in modern telephony, How numbering plan is a...

How numbering plan is achieved in modern telephony? Give the structure with example. The objective of numbering plan is to uniquely identify every subscriber connected to a tel

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