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

State the number of definitions of firewall, State the number of definition...

State the number of definitions of firewall Though there exist a number of definitions of firewall, in simplest terms it can be defined as "a mechanism used to protect a truste

Explain the message passing interface, Q. Explain the Message Passing Inter...

Q. Explain the Message Passing Interface? The Message Passing Interface (MPI) is a universal benchmark for providing communication among multiple simultaneous processes on a di

What are the advantages of open source system, What are the advantages of o...

What are the advantages of open source system? High-quality software Lesser hardware costs Integrated management No vendor lock-in Take control of our softwa

Existential construction - artificial intelligence, The English existential...

The English existential construction involves so-called there-sentences such as these: (1)  There is a dog in the yard (2)  There were no children at the party (3)  There

Datastructure, deque insertion and deletion ..

deque insertion and deletion ..

Pythagorean theorem, if the 6 is a and the b is 3 what is the c ?

if the 6 is a and the b is 3 what is the c ?

What is access latency and rotation speed, Q. What is Access latency and Ro...

Q. What is Access latency and Rotation Speed? Access latency: A disk access basically moves the arm to selected cylinder and waits for rotational latency that may take less t

Convert number to hexadecimal and decimal, Perform the following calculatio...

Perform the following calculations assuming that all numbers are stored in 16-bit registers as 2's complement binary numbers with no overflow provision. Convert each of the numbers

Explain the regular expression and transition diagram, State the relation a...

State the relation among Regular Expression, Transition Diagram and Finite State Machines. By using a simple instance establish your claim.   Answer: For each regular language,

Explain with the help of examples fifo algorithms, Explain with the help of...

Explain with the help of examples FIFO algorithms? FIFO policy: This policy easy removes pages in the order they arrived into the main memory. By using this policy we easily

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