Project ForgeGiven f(w,x,y,z) = Σm(0,1,2,3,7,8,10) + Σd(5,6,11,15), where d 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 = (w̄+z̄)(x̄+z)
- Bf = (w̄+z)(x+z)
- Cf = (w+z)(x̄+z)
- Df = (w+z̄)(x̄+z)
Explanation
Group the ZEROS (offset: m4,9,12,13,14) using don't-cares to help. Quad {m4,m6(dc),m12,m14}: rows wx=01&11 (x=1 constant) × cols yz=00&10 (z=0 constant) → sum term (x̄+z). Quad {m9,m11(dc),m13,m15(dc)}: rows wx=10&11 (w=1 constant) × cols yz=01&11 (z=1 constant) → sum term (w̄+z̄). These two quads cover all required zeros, giving the minimal POS: f = (x̄+z)(w̄+z̄), i.e. f = (w̄+z̄)(x̄+z).
Source: GATE CS 2017 (Session 2) (2017)
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