Simplify the Boolean function:
F (w,x,y,z) = ∑ (0, 1, 2, 3, 4, 6, 8, 9, 12, 13, 14) (8)
Ans: f(w, x, y, z) = ∑(0, 1, 2, 3, 4, 6, 8, 9, 12, 13, 14)
The above function is of four Boolean variables. The K-Map for this function is defined as in figure below. Minterms of four variables comprising decimal equivalent 0, 1, 2, 3, 4, 6, 8, 9, 12, 13 and 14 generate 1 as output for the function, thus squares corresponding to minterms 0000, 0001, 0010, 0011, 01000, 0110, 1000, 1001, 1100, 1101 and 1110 consist of an entry 1. The remaining squares consist of 0 as an entry.
So there is five quads: three marked along with closed rectangles and one wrapped around w' and z' and of four corners. Hence the given function can be expressed in simplified type as
f(w, x, y, z) = y'z' + w'x' + wy' + w'z' + xz'