Question

Digital Logic Design Lab

Prove the following Boolean Algebra theorems and properties by constructing Logic Circuits for each theorem/properties using our educational simulation software:

Q2-a) Prove that:            aa’ = 0

Q2-b) Prove that:           a+a’=1

Answer 1

Prove that: aa’ = 0

Prove that: a+a’=1

• aa'= 0 a variable AND’ed with its complement is always equal to 0
• a+ a' = 1 a variable OR’ed with its complement is always equal to 1

both are Complement law and it says that– A term AND´ed with its complement equals “0” and a term OR´ed with its complement equals "1" .

Here in this picture i am explaning how OR,AND, NOT operation work.

now here in this 2nd picture represetation using Logic Circuits for both given  theorem.

so in 1st digram of above image, I have mentioned Logic Circuits representation of  aa’ = 0 and in 2nd digram, I have mentioned Logic Circuits representation of a+a’=1 .

Note-

i have used one NOT GATE In both Logic Circuits representation