Match Boolean expressions P= X Y Z+ XY Z+ XYZ, Q=XYZ+X YZ+XY Z, R=XY+XYZ+XY Z+ XYZ, S= X YZ+ XYZ+X YZ+XYZ to K=X(Y+Z), L= X(Y+ Z), M=Z, N=Y(X+Z).

GATE 2020 BM – Question 45

Analog and Digital Electronics · Number Systems and Boolean Algebra · 2 marks · Multiple choice

Match Boolean expressions P=$\bar X\bar Y\bar Z+\bar XY\bar Z+\bar XYZ$, Q=$XYZ+X\bar YZ+XY\bar Z$, R=$XY+XYZ+XY\bar Z+\bar XYZ$, S=$\bar X\bar YZ+\bar XYZ+X\bar YZ+XYZ$ to K=$X(Y+Z)$, L=$\bar X(Y+\bar Z)$, M=Z, N=$Y(X+Z)$.

P–K,Q–L,R–N,S–M
P–L,Q–K,R–N,S–M
P–L,Q–N,R–M,S–K
P–M,Q–K,R–L,S–N

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Correct answer: (B) P–L,Q–K,R–N,S–M

Explanation

Factor P by X̄ and combine the ȲZ̄ and YZ̄ terms; this gives X̄(Z̄+Y)=L. Q factors to X(YZ+ȲZ+YZ̄)=X(Y+Z)=K. In R, XY absorbs XYZ and XYZ̄, then XY+X̄YZ=Y(X+Z)=N. S contains every X,Y minterm multiplied by Z, so S=Z=M. Therefore B.

GATE 2020 BM – Question 45

Explanation

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