Question $01(20$ marks$)$

Consider a $4$:$1$ multiplexer with two select inputs $($S$1$ and S$0)$ and four data inputs $($D$0,$ D$1,$ D$2,$ and D$3).$ Indicate any assumption that you make.

i$.$ Construct a truth table for a $4$:$1$ multiplexer.

$(05$ Marks$)$

ii$.$ Write the Boolean expression for the output $Y$ in terms of the select inputs and data inputs.

iii. Draw the logic diagram for the $4$:$1$ multiplexer.

$(04$ Marks$)$

iv$.$ Use a Karnaugh map to simplify the Boolean expression for Y$.$

$(05$ Marks$)$

$(04$ Marks$)$

v$.$ Write the simplified Boolean expression for $Y$ after simplifying it with the Karnaugh map.

$(02$ Marks$)$