CSE370 Assignment 1

Distributed: 5 January 2001
Due: 12 January 2001

Reading:

1. Katz, Chapter 1 (for an alternative to the introductory lecture).
2. Katz, Appendix A (pp. 650-661, this should be review).
3. Katz, Chapter 5.1 (pp. 241-248, this should also be review).

Exercises:

1. Familiarize yourself with the CSE 370 web pages. Participation in class accounts for what percentage of the final grade? How long should you spend on each homework problem before discussing it with others? What do you think of the collaboration/cheating policy? Does it seem reasonable? If not, what would you do differently? What question would you like to see on the course evaluation that is currently not on the list?
2. Make sure you have an NT account and can login to the machines in the instructional labs. Add yourself to the class mailing list using majordomo (if you choose to do so rather than just relying on the class e-mail archive).
3. Convert the following numbers to decimal:

(a) 0111001₂
(b) 0E5₁₆
4. Convert the following numbers to base 2:

(a) 127₁₀
(b) 40A₁₆
5. Perform the following operations (without converting to base 10):

(a) 01₂ + 001001₂ + 01010₂
(b) 010110₂ - 001100₂
(c) 101₂ * 010₂
6. Represent the following numbers in the indicated notation:

(a) -22 in 6-bit signed magnitude (1 sign bit and 5 bits for the magnitude)
(b) -22 in 6-bit 2s complement
(c) what are the smallest and largest numbers you can represent in 6-bit 2s complement notation
(d) represent the 6-bit 2s complement number 111010 as a 4-bit signed magnitude number
7. Derive the Boolean equations for the outputs d28, d29, d30, and d31 of the calendar subsystem example when the months are encoded from 0 to 11 instead of 1 to 12. Try to make the expressions as simple as possible exploiting don't cares as much as you can. Compare the 0 to 11 encoding with the 1 to 12 encoding in terms of the number of literals for each equation (in terms of m8, m4, m2, and m1 - not d28, d29, and d30). Which would you rather use and why?

Rationale:

• To review number systems.
• To gain familiarity with some of the basic concepts in digital logic.