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

Shape - elements of composition, Shape : A shape is any area that can b...

Shape : A shape is any area that can be perceived to have height and width. Shapes within an image can be created by the use of line, or by the edges created by variations in c

Add the equation by using 648 and 487 in bcd code, Add 648 and 487 in BCD c...

Add 648 and 487 in BCD code. Ans. In BCD Code, addition of 648 and 487: 6 4 8  =  0 1 1 0   0 1 0 0      1 0 0 0 4 8 7  =  0 1 0 0   1 0 0 0      0 1 1 1 ---------------------

What is the function of a tlb, What is the function of a TLB (translation...

What is the function of a TLB (translation look-aside buffer)? A small cache called the TLB is interporated into MMU, which having of the page table entries that correspondi

Fundamental change to the cloud to support mobility, Question: The abun...

Question: The abundance of resources and the ease of access to cloud computing can help to bridge the gap the resource gap for mobile computing. Nevertheless some fundamental c

Jewel polishing, Byteland county is very famous for luminous jewels. Lumino...

Byteland county is very famous for luminous jewels. Luminous jewels are used in making beautiful necklaces. A necklace consists of various luminous jewels of particular colour. Nec

Explain about the voice recognition system, Explain about the Voice recogni...

Explain about the Voice recognition system These voice recognition systems recognise spoken words e.g. for disabled people who can't use keyboards where they speak commands rat

Multisim simulation file, Build the circuit using the Asynchronous Counter ...

Build the circuit using the Asynchronous Counter Technique with JK FF and relevantgates capable of executing the counting sequence as {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}Simulate the cir

Advntages of parallel processing oversequential computation, Advntages of p...

Advntages of parallel processing oversequential computation Parallel computing has the following benefits over sequential computing: i)    Accumulate time ii)   Solves b

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