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

Propositional logic - artificial intelligence, Propositional Logic - artifi...

Propositional Logic - artificial intelligence: This is a limited logic, which permit  us to write sentences about propositions - statements about the world - which can either b

In ldb what determines hierarchy of the tables, In LDB what determines hier...

In LDB what determines hierarchy of the tables? Structure

Quick sort , Write Quick sort non recursive program

Write Quick sort non recursive program

Explain basic cpu structure, A computer manipulates data consistent with in...

A computer manipulates data consistent with instructions of a stored program. Stored program means that the data and program are stored in same memory unit. Central processing unit

Which type of web document is run at the client site, Which type of web doc...

Which type of web document is run at the client site? Active web document is a type of web document is run at client side.

Differentiate between sequential and combinational circuits, Problem 1 ...

Problem 1 Prove that :- x(x + y) = x by using identities 2 Write a short note on Analog to Digital Converter (ADC) 3 Differentiate between sequential and combinational ci

Develop a program which reads hexadecimal number, Q.  Develop a program, wh...

Q.  Develop a program, which reads Hexadecimal number from an input file & convert it into Octal, Binary, and Decimal. The O/P should be written to a file & displayed accordingly.

#title.sequential circuit, design modulo 12 up synchronous counter using t ...

design modulo 12 up synchronous counter using t flip flop

What is the use of cache memory, What is the use of cache memory? The u...

What is the use of cache memory? The use of the cache memories solves the memory access problem. In certain, when a cache is included on the same chip as the processor, access

What do you mean by shopping bots, Q. What do you mean by shopping bots? ...

Q. What do you mean by shopping bots? ANSWER: A shopping bot or buyer agent is an intelligent agent on a Web site that assists you, the customer, search the products and servic

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