$3$ PROBLEM $3$

$(40$ points$)$ Consider binary words of $4-$bit length, $w=b_4{b}_3{b}_2{b}_1,$ where the $b_{i}s$ are $1$ or $0.$ We say that $w$ has even parity if the number of ones is an even number, there are $0,2$ or $4$ ones in the word $w.$ If the number of ones is $1,$ or $3,$ we say that that $w$ has odd parity. Construct a digital circuit whose input is a binary word $w$ of length $4,$ and outputs $1$ if $w$ has even parity, $0$ if $w$ has odd parity.