A combinational circuit takes in a $5-$bit input ABCDE and generates a $2-$bit value PQ such that PQ

represents the distance between the two closest $1$s in the input. The distance is defined to be the

number of $0$s between the two closest $1$s$.$

For example, if ABCDE is $01011,$ then the distance between the two closest $1$s $($the two rightmost $1$s$)$

is zero, therefore, PQ$=00.$ If ABCDE is $10010,$ then the distance between the two closest $1$s is $2,$

therefore, PQ$=10.$

You may assume that the distance is always determinable from the given input. Therefore, inputs

such as $00000$ and $01000$ will not be supplied to this circuit.

Draw the K$-$maps for P and Q and write the simplified SOP expressions for P and Q$.$

Using the simplified SOP expressions for P and Q to implement the circuit, what is the output if the

circuit is fed with the input ABCDE$=00100?$