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

Write decoder functionality in only one statement in verilog, Write decoder...

Write decoder functionality in only one statement in verilog module decoder( // Outputs dout, // Inputs din ); input [3:0] din; output [15:0] dout;

Explain possible attacks on the wired equivalent privacy, Question : (a...

Question : (a) IEEE802.11 supports two types of network architecture, describe these architectures with the support of diagrams detailing the network components. (b) IEEE80

Dimensionality of interconnection network, Dimensionality of Interconnectio...

Dimensionality of Interconnection Network Dimensionality signify the arrangement of nodes or processing elements in an interconnection network. In linear network or one dimensi

First-order logic - artificial intelligence, First-Order Logic We, as h...

First-Order Logic We, as humans, have always prided ourselves on our ability to think things through for this reason things are out and come to the only conclusion possible in

Assembly directives and pseudo-ops, Assembly directives and pseudo-ops: ...

Assembly directives and pseudo-ops: Assembly directives are which instructions that executed by the assembler at assembly time, not by the CPU at run time. They can build the

Compare memory mapped i/o with i/o mapped i/o, Compare memory mapped I/O wi...

Compare memory mapped I/O with I/O mapped I/O. Memory Mapped I/O Scheme: In this scheme there is only one address space. Address space is stated as all possible addresses tha

What is dhcp and how it works, Full form of is DHCP: Dynamic Host Control P...

Full form of is DHCP: Dynamic Host Control Protocol. It is mainly used to bound MAC Addresses of system. Especially for Wireless System.

Explain dead code elimination, Explain briefly Dead code Elimination of the...

Explain briefly Dead code Elimination of the commonly used code optimization techniques Dead code Elimination: Code which is unreachable or which does not influence the pr

C++, what is polymorphism

what is polymorphism

Designing e-cash based system, How can it be achieved in designing e-cash b...

How can it be achieved in designing e-cash based system? E-cash is essentially an online solution.  The buyer must validate the coins by the issuer in order to get the purchase

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