For bits x, y and z, the function maj(x, y, z) is defined to be the majority vot

Question

For bits x, y and z, the function maj(x, y, z) is defined to be the majority vote, that is, if two or more of the three bits are 0, then the function returns 0, otherise it returns 1. Write the truth table for this function and derive the boolean function that is equivelant to maj(x, y, z).

Oay so i know how to write the truth table for this problem, but I am extremely lost on how you derive boolean functions from the truth tables. I imagine functionaility of maj(x, y, z), but I have no idea how. Thank you in advance.

Explanation / Answer

The truth table might look like

the k-map is

hence the expression of maj(x,y,z) from k-map

M = xy + xz + yz

x y z maj(x,y,z) 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1

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