Project ForgeDigital Logic
Boolean Algebra & Minimization
GATE 2007
Hard
Consider the following Boolean function of four variables: f(w,x,y,z) = Σ(1,3,4,6,9,11,12,14). The function is
- independent of one variable
- Bindependent of two variables
- Cindependent of three variables
- Ddependent on all the variables
Explanation
Decoding minterms (w x y z): 1,3,4,6,9,11,12,14 = 0001,0011,0100,0110,1001,1011,1100,1110. Pairing each minterm with its y-complement (flipping only the y bit) always lands on another minterm in the same set (1↔3, 4↔6, 9↔11, 12↔14) — meaning f's value never depends on y. So f is independent of exactly one variable, y.
Source: GATE CS 2007 (2007)
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