Design an $8$:$1$ multiplexer using a $3$ to $8$ decoder.Design a circuit that accepts a $3-$bit signed number $A_2{A}_1{A}_0.$ If the decimal equivalent value of

the number is less than or equal to $1,$ then the number is multiplied by $2.$ Otherwise, the value $2$

is added to the input number. Hint: what is the minimum number of outputs?

$($a$)$ Find the truth table of the circuit.

$($b$)$ Design a combinational logic circuit that implements the above circuit using a $3$ to $8$

decoder.