CSE370 Assignment 1

Distributed: 25 September 2000
Due: 2 October 2000

Reading:

1. Katz, Chapter 1 revised - handout (pp. 1-24).
2. (Optional) Katz, Chapter 1 (for an alternative to the introduction).
3. Katz, Appendix A (pp. 650-661, this should be review).
4. Katz, Chapter 5.1 (pp. 241-248, this should also be review).

Exercises:

1. Familiarize yourself with the CSE 370 web pages. The written assignments (such as this one) account for what percentage of the final grade? How long should you spend on each homework problem before discussing it with others? 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) 0011011₂
(b) 174₈
(c) 3F8₁₆
(d) 1101.1011₂
4. Convert the following numbers to base 2:

(a) 254₁₀
(b) 174₈
(c) 2.4375₁₀
(d) 0C5₁₆
5. Perform the following operations (without converting to base 10):

(a) 15₈ + 53₈
(b) 0001₂ + 1001₂ + 00111₂
(c) 110100₂ - 011010₂
(d) 101₂ * 011₂
6. Represent the following numbers in the indicated notation:

(a) -26 in 6-bit signed magnitude (1 sign bit and 5 bits for the magnitude)
(b) -26 in 6-bit 2s complement
(c) what are the smallest and largest numbers you can represent in 8-bit 2s complement notation
(d) represent the 8-bit 2s complement number 11111100 as a 4-bit 2s complement number
7. The digits of a 4-bit 2s complement number can be represented by the variables X₈, X₄, X₂, and X₁, respectively.
   (a) Determine the Boolean expression for -6₁₀ represented as a 4-bit 2s complement number using the 4 variables.
   (b) Draw a logic circuit corresponding to your expression for the previous problem.
8. Find the state table for the state diagram we derived in class for the modified combination lock (see slide #45 in the Introduction lecture notes). Do not worry about coming up with a state encoding. A symbolic state table will do.

Rationale:

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