$9\mathrm{.}1.$c Logic Circuit Design with $74155$ Decoder configured as a $2-$to$-4-$line Decoder

A combinational circuit has two inputs $\backslash ($ X$,$ Y $\backslash )$ and an output $\backslash ($ F $\backslash )$ which is:

$\backslash [$

F$=$X$^\{\backslash$prime$\}$ Y$+$X Y$^\{\backslash$prime$\}$

$\backslash ]$

i$)$ Design a circuit in Proteus program that generates F using a $74155$ decoder and an external NAND gate.

ii$)$ Obtain the truth table of the circuit.