Question $1(25\%)$

Design a system that has as its inputs a number from $1$ to $10$ and provides as its outputs $($A$,$ B$,$

C$,...,$ H$)$ the signals to drive the display described below.

The inputs are labeled W$,$ X$,$ Y$,$ and Z and are normal binary. The input combinations $0000,1011,$

$1100,1101,1110,$ and $1111$ will never occur; they are to be treated as don$$t care.

The display allows for the representation of Roman numerals $($except that IIX is used to represent

$8,$ whereas it is usually written as VIII$).$ The figure above shows that the display has eight segments

labeled A through H$.$

There are two ways to represent a numeral on this display $$ left and right. For example, to represent

a $5$ on this display, light segments A and C $($or E and G$)$ are for the left representation, and the

right representation is for light segments B and D $($or F and H$).$

The following illustration shows all digits as they should be coded for each, with a lit segment

represented by a bold line and an unlit segment represented by a dashed line.