Write both a PDA and a CFG for the language $($page $80)$:

$C=\{\begin{array}{ccc}\text{w}\text{i}\text{n}& \{0,& 1{\}}^{**}|w\end{array}$ has an equal number of $0$s and $\{$:$1s\}.$

Please include a brief explanation of why they work. $($If you convert a PDA

to a CFG or vice versa, that suffices as an explanation.$)$