Q$2/$ Consider two $2-$bit numbers:

$($a$)$ Create a truth table that calculates the results of both addition and multiplication operations for two $2-$bit numbers. Include an additional input column to toggle between these two operations, resulting in a total of $5$ input columns. The output of the truth table should represent the outcomes of these operations, with addition results represented by three bits and multiplication results by four bits. $(10\%)$