1. Explain why modern machines consist of multiple levels of virtual machines. Why not just have two levels, the digital logic level and the high-language programming level? 

2. Given a (very) tiny computer that has a word size of 6 bits, what are the smallest negative numbers and the largest positive numbers that this computer can represent in each of the following representations?

a. Signed magnitude
b. One's complement
c. Two's complement

3. Convert the followings:

a. AC1216 to binary
b. -10710 to 8-bit 2's Complement
c. 11001101012 to Hexadecimal
d. 100111102 (8-bit 2's complement representation) to decimal

4. A Computer uses IEEE-754 format to represent floating points. What value ( in decimal) the computer represents if the floating point is represented using the following binary digits:
11000001010100000000000000000000

5. Charles Sturt University (CSU) academic director want to hire a lecture in Sydney Study Center. The applicant has worked in three universities before; University of New South Wales (UNSW), Macquarie University, and Sydney University. Before he will hire him, he must get input from these three universities. After few weeks of receiving feedback from all three, he has come to the following conclusions:

· Hire if two of them say yes and one says no.
· Hire if all of them say yes.
· Don't hire otherwise.

Construct a truth table and find the minimized Boolean function to implement the logic telling the director when to hire. Draw a circuit diagram for the Boolean function. [6 marks]