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

An algorithm, find cos(x) and sin(x) an pseudocode (while loop

find cos(x) and sin(x) an pseudocode (while loop

Static and dynamic interconnection network, Static and Dynamic Interconnect...

Static and Dynamic Interconnection Network In a static network the connection among input and output nodes is permanent and cannot be changed. Static interconnection network ca

Minimum and maximum algorithm, For this assignment, you will need to create...

For this assignment, you will need to create an ARM assembly language code routine that implements an algorithm to search through an array and find BOTH the minimum and maximum val

Explain about microprocessors, Q. Explain about Microprocessors? Microp...

Q. Explain about Microprocessors? Microprocessors have instruction sets ranging from 20 to several hundred instructions, known as microprograms, which are stored in ROM to init

Combinatorial and scheduling problems, Combinatorial and Scheduling Proble...

Combinatorial and Scheduling Problems: One class of problems is concerned with specifying optimal scheduled. A classical example is the Travelling Salesperson Problem where

Define race condition, Define race condition.  When several process acc...

Define race condition.  When several process access and manipulate similar data concurrently, then the outcome of the implementation depends on particular order in which the ac

What are the kernel threads, What are the Kernel threads Kernel threads...

What are the Kernel threads Kernel threads are supported directly by the operating system .Thread creation; scheduling and management are done by the operating system. Thus the

Specifying research problems, Specifying Research Problems: In our age...

Specifying Research Problems: In our agent terminology or in technique history, a problem to be solved is a specific and justified manner where the agent has starts with the b

Illustrate 16-bit isa, Illustrate 16-bit ISA?  Compare it with 8-bit ISA bu...

Illustrate 16-bit ISA?  Compare it with 8-bit ISA bus.  The only difference between 8 and 16-bit ISA bus is that an extra connector is attached behind the 8-bit connector. 16-b

Explain difference between security and protection, Explain difference betw...

Explain difference between Security and Protection? Protection mechanism: The subsequent mechanisms are commonly utilized for protecting files having programs and data. (a

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