Assignment: Data representation & Digital logic

1. Using a "word" of 5 bits, list all of the possible signed binary numbers and their decimal equivalents that are represent able in:

a. Signed magnitude

b. One's complement

c. Two's complement

2. 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:

1 10000011 11000000000000000000000

3. Using Boolean algebra, prove that:

X'Y + XYZ' + Y' + XZ (Y+Y') = 1

4. Charles Sturt University (CSU) has opened an IT Doctorate study in Sydney Study Centre. The applicant should has a master degree in IT or a master degree in electrical engineering. The applicant should also has completed project subject (e.g. ITC570, ITC571, ...) in his master degree. Before CSU management staff approve student's application, they have to check student master degree if it meet the requirements and also check if the student completed project subject or not in his master degree. After checking applicant documents, CSU staff has come to the following conclusions:

• Approve if applicant has one of the required master degrees and has completed project subject.
• Approve if applicant has two of the required master degrees and has completed project subject.
• Don't approve otherwise.

Construct a truth table and find the minimized Boolean function to implement the logic telling the CSU staff when to approve. Draw a circuit diagram for the Boolean function.

5. Complete the truth table for the following sequential circuit