traffic logic controller has $4$ inputs A$,$ B$,$ C$,$ and D$.$ The controller has two outputs, which are

the intersection lights. There is an east$-$west $($EW$)$ light and north$-$south $($NS$)$ light. Inputs A and B are a

$2-$bit unsigned binary number with A being the MSB$,$ and C and D are another $2$ bit binary unsigned

number with C being the MSB$.$ The logic of the controller works as follows:

$$ If the number AB is greater than the number CD$,$ the EW light is OFF and NS is ON

$$ If the number CD is greater than the number AB$,$ the NS is OFF and the EW is ON

$$ If the number AB is equal to number CD$,$ EW light is OFF and NS is O