a$.$ Name the segments from A to F$,$ starting with the top segment and going clockwise. Name the inputs D$3$ D$2$ D$1$ D$0.$ The inputs encode decimal values from $0$ to $9.$ Write a truth table with D$3$ D$2$ D$1$ D$0$ as inputs and $A$ to $F$ as outputs, according to the above drawing. For inputs that do not represent decimal digits, put "dont'care" symbols as outputs in the truth table.

b$.$ Draw the $K-$maps for the outputs. Use the $K-$maps to minimize the equations. Write the resulting sum$-$of$-$products equations.

c$.$ Draw the circuits according to the previous minimized equations.