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

Convert the decimal number to excess-3 code, Convert the decimal number 430...

Convert the decimal number 430 to Excess-3 code ? Ans. Excess  3  is  a  digital  code  acquired  from  adding  3  to  every  decimal  digit  and  after that converting the res

What are vectored interrupts, What are vectored interrupts? To decrease...

What are vectored interrupts? To decrease the time involved in the polling process, a device requesting an interrupt may recognize itself directly to the processor. Then the pr

Emergence of computer network, Which Technologies of this age had tended to...

Which Technologies of this age had tended to the emergence of computer network? Ans: The technologies are Communication technology and Computer technology with the support of V

An example of load-store optimization using expression trees, Give LOAD-STO...

Give LOAD-STORE optimization based on expression trees for the expression (A+B)/(C-D). LOAD-STORE optimization based on expression trees for the expression (A+B)/(C-D) is given

What is virtual memory, Virtual Memory is a way of extending a computer's m...

Virtual Memory is a way of extending a computer's memory by using a disk file to replicate add'l memory space. The OS remain track of these add'l memory addresses on the hard disk

Explain the various interface circuits, Explain the various interface circu...

Explain the various interface circuits.  An I/O interface having of circuitry required to connect an I/O device to computer bus. One side having of a data path with its associa

Java database connectivity, Java Database Connectivity (JDBC) With two...

Java Database Connectivity (JDBC) With two different types of technologies available in the market today viz., the Windows and the Java technologies developed by the Microsoft

Example multi-layer ann with sigmoid units, Example Multi-layer ANN with Si...

Example Multi-layer ANN with Sigmoid Units - Artificial intelligence: We will discuss ourselves here with ANNs containing only 1 hidden layer, as this makes describing the back

Operations from events, Operations from events During analysis, events...

Operations from events During analysis, events which are sent to target objects. An operation on these object are presented as labels on transitions and should not be explicit

Perceptrons of artificial neural networks, Perceptrons: However the we...

Perceptrons: However the weights in any ANN are usually just real numbers and the learning problem boils down to choosing the best value for each weight in the network. Becaus

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