Consider a Boolean function f(w, x, y, z). Suppose exactly one input is…

GATE · 2006 · CS

Consider a Boolean function f(w, x, y, z). Suppose exactly one input is allowed to change at a time. If f is true for two input vectors i1 = (w1, x1, y1, z1) and i2 = (w2, x2, y2, z2), and i1 and i2 differ in exactly one bit position, we want f to remain true during the transition without becoming false momentarily. Let f(w, x, y, z) = ∑(5, 7, 11, 12, 13, 15). Which of the following cube covers of f ensures this required property?

  1. A.

    w'xz, wxy', xy'z, xyz,wyz

  2. B.

    wxy,w'xz,wyz

  3. C.

    wx(yz)', xz, wx'yz

  4. D.

    wxy', wyz, wxz, w'xz, xy'z, xyz

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