A$)$ Design a $2-$bit comparator in the Equal output that only goes high when the two $2-$bit inputs are equal, and the Greater output turns high when $A>B($as shown$)$

Show your gate$-$level design

B$)$ Add the following binary numbers and identify if there is a carry or an overflow $($verify the results with their decimal values$)$:

$0001+1100$

$0101+1101$

$11001111+10100001$

$01101100+01010011$

C$)$ Add the following $2\text{'}$s complement numbers and identify if there is a carry or an overflow $($verify the results with their decimal values$)$:

$0001+1100$

$0101+1101$

$11001111+10100001$

$01101100+01010011$

D$)$ Design an $8-$bit ripple carry adder using half and full adder circuits:

E$)$ Design a binary $4-$bit ALU with $4$ functions ADD, AND, NAND, and XNOR $($bit$-$compare$)$ as shown: