$($a$)$ Design a suitable combinational logic circuit that detect decimal number, $x($represented in its equivalent input binary values from $0$ to $15)$ whereby the output is HIMI when otherwise, the output is LOW. Do the following. Show all working steps.

Marks

i$)$ Draw the truth table.

ii$)$ Simplify the Boolean expression into POS expression using K$-$Map.

iii$)$ Construct the OR$-$AND logic cireuit.

iv$)$ Construct the logic circuit using only NOR gates.