$2\text{'}$s complement Logic is a circuit that converts the input to its corresponding $2$'complment binary representation. For example, when input is binary number ${001}_2,$ the $2\text{'}$s complement representation is ${111}_2.$ When input is binary number ${110}_2,$ the $2\text{'}$s complement representation is ${010}_2.$

$($a$)$ Based on the description above, construct the Truth Table of a $3-$bit $2\text{'}$s complement Logic Circuit.

$\backslash$table$[[$Input$,2\text{'}$s Complement$],[A_2,A_1,A_0,B_2,B_1,B_0$