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

C programming, You are given a collection of words, say as in a dictionary....

You are given a collection of words, say as in a dictionary. You can represent it in the following compressed form: the first word will be followed by a sequence of a pair of numbe

Assembler directives, Assembler directives: An assembler directive is ...

Assembler directives: An assembler directive is a statement to give direction to the assembler to perform the task of assembly process. Assembler directives control organizati

Transaction that are programmed by the user, How the transaction that are p...

How the transaction that are programmed by the user can be protected? By executing an authority check.

Registers used in organisation of an associative memory, In the organisatio...

In the organisation of an associative memory, many registers are used: Comparand Register (C): This register is used to grasp the operands, which are being searched for, or

Explain overlay structured program, Explain overlay structured program ? ...

Explain overlay structured program ? A program having overlays is termed as overlay structured program, here an overlay is a part of program that has similar load origin as som

Planning too much up front a mistake in an oosad, You can't plan only for t...

You can't plan only for the present phase of the project as your future activities are still coarse granular. To have good planning you require to have fine granularity w.r.t the t

Observing the existing system first hand, Observing the existing system fir...

Observing the existing system first hand This involves watching personnel using the existing system to find out precisely how it works. There are a number of disadvantages as

Micro processor code, Suppose that the working register W contains the valu...

Suppose that the working register W contains the value 0x4F, the register FSR contains the value 0x2B; the register with address 0x2B contains 0x2F and the instruction ADDWF INDF,

What is logical address space and physical address space, What is logical a...

What is logical address space and physical address space? The set of all logical addresses generated by a program is known as a logical address space; the set of all physical a

Artificial neural networks - artificial intelligence, Artificial Neural Net...

Artificial Neural Networks - Artificial intelligence: Decision trees, while strong, are a easy representation method. While graphical on the surface, they may be seen as disjun

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