For F(w,x,y,z)=wy+xy+ wxyz+ w xy+xz+ x y z, find the complete set of essential prime implicants.

$w,y,xz,\overline x\overline z$

$y,\overline x\overline y\overline z$

GATE 2014 EC (EC1) – Question 51

Digital Circuits · Combinatorial Circuits · 2 marks · Multiple choice

For $F(w,x,y,z)=wy+xy+\overline wxyz+\overline w\overline xy+xz+\overline x\overline y\overline z$, find the complete set of essential prime implicants.

$w,y,xz,\overline x\overline z$
$w,y,xz$
$y,\overline x\overline y\overline z$
$y,xz,\overline x\overline z$

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Correct answer: (D) $y,xz,\overline x\overline z$

Explanation

Combine wy with the two w̄ terms containing y to obtain y, and absorb xy into y. The function becomes y+xz+x̄z̄. Each implicant covers an exclusive minterm: y at x=0,z=1,y=1; xz at x=z=1,y=0; x̄z̄ at x=z=0,y=0. Hence all three are essential: **y,xz,x̄z̄,D**.