Determine Boolean identities using Boolean algebra, Computer Engineering

Assignment Help:

Prove the following identities
 
a. A
‾B‾C‾ + A‾BC‾ + AB‾C‾ + ABC‾ = C
b. AB + ABC + A
‾ B + AB‾C = B + AC

Ans.

a. LHS = A'B'C' + A'BC' + AB'C' + ABC'
= A'C' (B' + B) + AC' (B' + B)
= A'C' + AC'   [as B'+B = 1]
= C' (A' + A)
= C'                   [since A'+A =1]
= RHS.
Thus Proved

b. LHS = AB + ABC + A'B + AB'C

= B + AC
= B (A + A') +  AC (B + B')
= B + AC   [as B + B' = A + A' = 1]
= B + AC
= RHS.
Thus Proved


Related Discussions:- Determine Boolean identities using Boolean algebra

Grounding a variable - first-order logic, Grounding a variable - first-orde...

Grounding a variable - first-order logic: The perform of making ourselves clear about a variable by introducing an exists or a forall sign is called quantifying the variable.

Design a half adder, Q. Design a half adder? In half adder inputs are: ...

Q. Design a half adder? In half adder inputs are: The augend let's say 'x' and addend 'y' bits. The outputs are sum 'S' and carry 'C' bits. Logical relationship betwee

Describing Random Algorithm, Suppose you''re given n numbers and asked to f...

Suppose you''re given n numbers and asked to find a number that is greater than or equal to the median a) What is the lower bound for the worst case complexity of this problem?

What is matrix addressing mode, What is Matrix Addressing Mode. Ans. M...

What is Matrix Addressing Mode. Ans. Matrix Addressing Mode: The arrangement which needs the fewest address lines is a square array of n rows and n columns for a whole memory

Short notes on model primitives in director mx 2004, Question: (a) Prep...

Question: (a) Prepare short notes on the model primitives in Director MX 2004. (b) Therefore using the box primitive write codes to prepare a new model resource of length 50

:P, My name is mrs flo and i apporve dubstep, do you apporve it?

My name is mrs flo and i apporve dubstep, do you apporve it?

How do you split hydrogen and oxygen gases, Q. How do you split Hydrogen an...

Q. How do you split Hydrogen and Oxygen gases in industrial electrolysis of water process? Answer:- In oxygen, electrolysis and hydrogen gas are produced at different elec

What is the use of the statement leave to list-processing, What is the use ...

What is the use of the statement Leave to List-processing? Leave to List-processing statement is used to make a list from a module pool.  Leave to list processing statement per

What are the advantages of using uml, Benefits of using UML breaks the comp...

Benefits of using UML breaks the complex system into discrete pieces that can be understood simply. Handover the system to new team becomes simpler. Complex system can be un

Write the game using writing functions, The year is 2199. For many generati...

The year is 2199. For many generations, the robotic Cyleth have faithfully served humanity. However, under the direction of the computerized superintelligence Skyweb, they have tur

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