a$)$ "Quark" is an annual technical festival organized by the Goa Campus of BITS Pilani

in February every year. This year, as part of a hardware design competition,

participants were given the task of creating a seatbelt warning system for cars. The

system should generate an alarm signal if a person is driving the car and the seat belt

is not fastened. To build this system, you need to determine the number of inputs and

outputs required. $($Hint: The alarm should not be generated if the key is not in the

ignition or if there is no person sitting behind the wheel.$)$ Also, provide the truth

table, Boolean equation, and gate$-$level schematic diagram.

b$)$ Consider F$=$A$^(\text{'})$B$^(\text{'})$C$^(\text{'})+$A$^(\text{'})$B$^(\text{'})$C$+$A$^(\text{'})$BC$+$AB$^(\text{'})$C$+$ABC. Simplify the expression

using the laws of Boolean algebra. Show each step, postulates, and theorems used.

Draw the logic diagram for the simplified expression using NAND gates only.

c$)$ Consider a $16$KB$,$ byte addressable RAM chip. Answer the following questions.

a$.$ What is the address space and addressability of the memory?

b$.$ What is the number of address bits needed?