Project ForgeGiven the following Karnaugh Map for a Boolean function F(w,x,y,z), with rows wx=00,01,11,10 and columns yz=00,01,11,10: row00=[1,0,0,1], row01=[0,1,1,0], row11=[0,1,1,0], row10=[1,0,0,1]. Which one or more of the following Boolean expression(s) represent(s) F?
- w̄x̄ȳz̄ + wx̄ȳz̄ + w̄x̄yz̄ + wx̄yz̄ + xz
- Bw̄x̄ȳz̄ + w̄x̄yz̄ + wx̄yz + xz
- Cw̄x̄ȳz̄ + wx̄ȳz̄ + wx̄ȳz + xz
- x̄z̄ + xz
Explanation
Reading the K-map, F=1 exactly when x=z (both cases x=0,z=0 and x=1,z=1), independent of w and y entirely — F = x̄z̄+xz, matching option D directly. Option A's first four terms telescope via w̄+w=1 to x̄ȳz̄+x̄yz̄=x̄z̄, and combined with its xz term gives exactly x̄z̄+xz — also correct. Option B contains the specific term wx̄yz (minterm w=1,x=0,y=1,z=1, i.e. x≠z), which is NOT in the true F (F=0 there) — incorrect. Option C contains wx̄ȳz (x≠z, also wrongly included) and its first two terms only cover x̄ȳz̄ (missing the required x̄yz̄ minterms) — incorrect.
Source: GATE CS 2025 (Session 2 / CS2) (2025)
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