Given \(f(w, x, y, z) = \Sigma_m(0,1, 2, 3, 7, 8, 10) + \Sigma_d(5, 6, 11,…

GATE · 2017 · CS · Set 2 · Computer Science & IT

Given f(w,x,y,z)=Σm(0,1,2,3,7,8,10)+Σd(5,6,11,15)f(w, x, y, z) = \Sigma_m(0,1, 2, 3, 7, 8, 10) + \Sigma_d(5, 6, 11, 15); where dd represents the 'don't-care' condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of f(w,x,y,z)f(w, x, y, z)?

  1. A.

    f=(wˉ+zˉ)(xˉ+z)f=(\bar{w}+\bar{z}) (\bar{x}+z)

  2. B.

    f=(wˉ+z)(x+z)f=(\bar{w}+z) (x+z)

  3. C.

    f=(w+z)(xˉ+z)f=(w+z) (\bar{x}+z)

  4. D.

    f=(w+zˉ)(xˉ+z)f=(w+\bar{z}) (\bar{x}+z)

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