boolean - XOR Majority Algebraic Logic -


how implement majority function xor , and only? enter image description here how authors of paper equation present below?

a majority function 3 inputs can written cnf (product of sums)

(a or b) , (a or c) , (b or c)

or dnf (sum of products)

ab or ac or bc

using , and xor, can write

maj(a,b,c) = ab xor bc xor ac

a truth-table easiest way check this. xor 3 inputs true, if either 1 input true or 3 inputs. 

             ab        00  01  11  10       +---+---+---+---+    0  | 0 | 0 | 1 | 0 | c     +---+---+---+---+    1  | 0 | 1 | 1 | 1 |       +---+---+---+---+

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