In the following binary modulation system, a logical $1$ is $1$ volt and a logical $0$ is $0$ volts.

$($a$)$ Write the equations for $\backslash (\backslash$phi$($t$)\backslash )$ for all combinations of the three$-$bit word $\backslash (\backslash$mathrm$\{$C$\}$ B A $\backslash ).$

$($b$)$ Draw the constellation diagram for the signal $\backslash (\backslash$phi$($t$)\backslash ).$