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

State about the logic micro-operations, State about the Logic Micro-operati...

State about the Logic Micro-operations These operations are performed on binary data stored in register. For a logic micro-operation each bit of a register is treated as a diff

And-introduction rule, And-Introduction: In generally English says tha...

And-Introduction: In generally English says that "if we know that a lot of things are true, so we know that the conjunction of all of them is true", then we can introduce conj

Convert the following binary numbers into octal, Q. Convert the following B...

Q. Convert the following BINARY numbers into OCTAL, double check by converting the result OCTAL to BINARY. a) 111.111 b) 10110111 c) 0.11111

Show types under which networks will be divided, What are the two broad typ...

What are the two broad types under which Networks will be divided? Ans: All computer networks fit in one of the two dimensions specifically: a) Transmission Technology, thi

Reading decision trees - artificial intelligence, Reading Decision Trees ...

Reading Decision Trees There is a link between decision tree representation and logical representations, which may be exploited to form it more easy to understand and learned

Name the 7400 series TTL chip, Name the 7400 series TTL chip which is a pri...

Name the 7400 series TTL chip which is a priority encoder. Write its truth table. Ans. Available IC in 74 series is 74147 that is a priority encoder. Such I

Constructor, what is meant by private copy constructor

what is meant by private copy constructor

Defined for a push button fields in the screen attributes, What is to be de...

What is to be defined for a push button fields in the screen attributes? A function code has to be described in the screen attributes for the push buttons in a screen.

Show two way pipelined timing, Q. Show Two Way Pipelined Timing? Figure...

Q. Show Two Way Pipelined Timing? Figure below demonstrates a simple pipelining scheme in which F and E stages of two different instructions are performed concurrently. This sc

Explain internal organization of bit cells in a memory chip, Explain with n...

Explain with neat diagram the internal organization of bit cells in a memory chip. Memory cells are usually organized in the form of an array, in which every cell is capable of

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages