$2$ PROBLEM $2$

$(20$ points$)$ Consider two binary words of $4-$bit length:

$w_1=b_4{b}_3{b}_2{b}_1,$ and $,w_2=a_4{a}_3{a}_2{a}_1,$

where the $a_i,b_{i}in\{0,1\}.$ Construct a digital circuit using OR$,$ XOR, AND, and NOT gates that outputs

$1if{w}_1=w_2$

$0if{w}_1{w}_2.$

Remember that $w_1=w_2$ means that $b_4=a_4,b_3=a_3,b_2=a_2,b_1=a_1,$ and $w_1{w}_2$ means that there is an index i such that $b_i{a}_i.$

Hint. If $w_1=b_1$ and $w_2=a_1,$ then, the required circuit can be implemente using an XOR gate.