Question # $3$: $($ILOs based NARS $2018$: A$1,$ B$2$; ABET OUTCOME: $1,2)$

$(8$ Marks$)$

$($a$)$ Design a $81$ Multiplexer using only $21$ Multiplexers and any additional logic gates if necessarily.

$($b$)$ Design a combinational circuit of Bank customer$-$coding unit. The logic circuit has three binary inputs, $A,B$ and $C$ representing customer state and three binary outputs, $x,Y$ and $Z$ for the code.

When the binary inputs are equivalent to $0,1,2,$ or $3>$ Then the binary output is equivalent to the $($input $+2)$

When the binary inputs are equivalent to $4,5,6,$ or $7>$ Then the binary output is equivalent to $($input $-3).$ SOP expression of each output, $x,Y$ and $Z$ using Karnaugh map, then Sketch the simplified logic circuit of each output using logic gates