A combinational circuit is used to control a seven$-$segment display of decimal digits,

as shown in Figure $12\mathrm{.}37.$ The circuit has four inputs, which provide the four$-$bit code

used in packed decimal representation $(0_{10}=0000,$dots,$9_{10}=1001).$ The seven

outputs define which segments will be activated to display a given decimal digit. Note

that some combinations of inputs and outputs are not needed.

a$.$ Develop a truth table for this circuit.

b$.$ Express the truth table in SOP form.

c$.$ Express the truth table in POS form.

d$.$ Provide a simplified expression.

Design a $4-$to$-1$ multiplexer.

$($b$)$

Figure $12\mathrm{.}37$ Seven$-$Segment LED Display Example