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 ale and explain the functions of ale in 8085, ALE-> Address latch e...

ALE-> Address latch enable...In the case of microcontroller (8051)& microprocessor 8085 the data line and low order 8 bit address lines are multiplexed. In order to getting address

Move the layout table, You can select and move a layout table to other area...

You can select and move a layout table to other areas in a particular document. You can't, though, move a layout table so that it overlaps another. Next you will move the table

What is the efficient data structure used in rdbms, In RDBMS, what is the e...

In RDBMS, what is the efficient data structure used in the internal storage representation? B+ tree. Because in B+ tree, all the data is kept only in leaf nodes, that makes sea

How optimization is achieved in dns, How optimization is achieved in DNS? ...

How optimization is achieved in DNS? Two primary optimizations used in DNS and they are: replication and caching. All root servers is replicated; various copies of the server

What is usb, What is USB USB (UNIVERSAL SERIAL BUS) is intended to conn...

What is USB USB (UNIVERSAL SERIAL BUS) is intended to connect peripheral devices like mouse, keyboards, modems and sound cards to microprocessor through a serial data path and

Define access time for magnetic disk, Define access time for magnetic disk....

Define access time for magnetic disk. The sum of seek time and rotational delay is known as access time for disks. Normal 0 false false false EN-IN

Find two negative polarity items - artificial intelligence, This question c...

This question can be answered either with respect to English or with respect to a language other than English. (If you you are not a native speaker of the language of your choice,

What is compound statement, What is compound statement If we wish to ha...

What is compound statement If we wish to have more than one statement following the if or the else, they should be grouped together between curly brackets. Such a grouping is c

Explain cache organisation, Q. Explain Cache Organisation? Cache memori...

Q. Explain Cache Organisation? Cache memories are found in nearly all latest computers.  They are very helpful for increasing speed of access of information from memory.  Let's

Illustrate the history of computers, Q. Illustrate the history of computers...

Q. Illustrate the history of computers? Let's now consider history of computers since this will give fundamental information about technological development trends in computer

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