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

Area under curve , Write a program to find the area under the curve y = f(x...

Write a program to find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. The area under a curve between two points can b

What is gustafsons law, Q. What is Gustafsons Law? Amdahl's law is app...

Q. What is Gustafsons Law? Amdahl's law is appropriate for applications where response time is significant. On the other hand there are numerous applications that necessitate

Target _self, TARGET = "_self" "_self" puts the new document in the s...

TARGET = "_self" "_self" puts the new document in the same window and frame as current document. "_self" works the same as if you hadn't used TARGET at all.

Define parity bit and list its types, Define parity bit and List its types....

Define parity bit and List its types. The most common error detection code used is the parity bit. Parity bit is a extra bit contained with a binary message to make the total n

Propositional truth tables, Propositional truth tables: There {X\t} is...

Propositional truth tables: There {X\t} is a substitution that replaces all occurances of variable X with a term representing an object t as:  ∀X. A is true if and only

Linear model., what is linear model and its type

what is linear model and its type

Propositional model, Propositional model: Hence a propositional model ...

Propositional model: Hence a propositional model was simply an assignments of truth values to propositions. In distinguish, a first-order model is a pair (Δ, Θ) where

What qualifications needs to be an security professionals, Qualifications o...

Qualifications of security professionals For the security professionals, it is essential that they have adequate freedom to check the security measures and enforce them and

Define the do while loop, The do while Loop This is very similar to the...

The do while Loop This is very similar to the while loop except that the test occurs at the end of the loop body. This guarantees that the loop is executed at least once before

Computer, is data bus is bidirectional

is data bus is bidirectional

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