Design seven$-$segment decoder circuits for common cathode and common anode type with and without including don$$t care elements using Multiplexer.

$$ a$\mathrm{.}16$:$1$ Multiplexer

$$ b$\mathrm{.}8$:$1$ Multiplexer

Show the internal circuits of the above Multiplexer using$$

a$.4$:$1$ Multiplexer

b$\mathrm{.}2$:$1$ Multiplexer