$1)$ Design a $3$X$8$ decoder using AND, OR and NOT gates. Show the circuit.

$2)$ Design a $1-$bit adder that has three inputs $($A$,$ B$,$ and Cin$)$ and two outputs $($S and Cout$).$ S represents

the $$sum$,$ and Cout is the $$carry$.$ Write the TT$,$ K$-$map, and the equa$$ons for this component.

$3)$ Design a MUX with $2$ inputs and $1$ output. Use this to build a $4$X$1$ MUX. Use the la$$er to build a $8$X$1$

MUX. In addi$$on$,$ build a $8$x$1$ MUX using $2$X$1$ MUX$$s only.

$4)$ Design a component that determines the sign of a $8-$bit number.

$5)$ Using a $2$X$1$ MUX, create an absolute value component. The inputs are $8$ bits each, and the output is

also $8-$bits. Reserve the MSB for sign designa$$on$.$

$6)$ Draw a $1$X$4$ DeMUX with an enable bu$$on$.$

$7)$ Draw a majority selector with $4$ inputs and one output. If the majority of the inputs are $1,$ the

output F $=1,$ otherwise F $=0.$