Question

Simplify the given Expression

Y=ABC+AB’C+A’BC+BC’​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

A′B′C+A′BC′+AB′C′+ABC=A′B′C′+ABC+A′BC′+AB′C′

C(A′B′+AB)+C′(A′B+AB′)

C((A′B′+AB)′)′+C′(A′B+AB′)

Using Demorgan’s Law

C((A+B)(A′+B′))′+C′(A⊕B)

C(AA′+AB′+BA′+BB′)+C′(A⊕B)

C(0+AB′+A′B+0)′+C′(A⊕B)

C(AB′+A′B)+C′(A⊕B)

C(A⊕B)′+C′(A⊕B)

Now let assume  (A⊕B)=X  

CX′+C′X

Which is  C⊕X  

Or  X⊕C  

Now substituting back  X=(A⊕B) , we get

(A⊕B⊕C)  

which is required simplification

Where  ⊕  denotes  XOR

Explanation: