MC48 Homework 3 (Fall 1996)

Due: October 3, 1996

Note that I plan to do at least exercise 4.33, and probably also exercise 4.31 and/or part or all of 4.34 in class. Their inclusion in the homework assignment just means that you need to clearly write up what we've done in a more casual oral style in class.
  1. Do exercise 4.9 on page 304.
  2. Do exercise 4.31 on page 308; the reference to page 202 should be to pages 224-226.
  3. Do exercise 4.32 on page 308.
  4. Do exercise 4.33 on page 308. Where the problem statement refers to page 200, that should be page 223. In this and the following two exercises, remember that as many equations as necessary can be calculated simultaneously, so long as their inputs are all available. For example, initially all the ai and bi inputs are available at time 0, and so is c0, so during the first time unit (T), all of the pi and gi can simultaneously be calculated, so that at time T, they are now all available, and all the equations using them can simultaneously be calculated. Here, in concise form, are the ground rules:
  5. Do exercise 4.34 from page 263. The reference to page 202 should be to pages 225-226. The three options you are to compare can be restated as follows:
    1. Sixteen one-bit adders hooked together in ripple-carry fashion.
    2. Four four-bit adders hooked together in ripple-carry fashion. Inside each of the four-bit adders, however, the carry lookahead is used.
    3. Four four-bit adders hooked together in carry lookahead fashion. As in the previous option, carry lookahead is used within each of the four-bit adders as well.
  6. Do exercise 4.35 from page 308. The four options to compare can be restated as follows:
    1. Sixty-four one-bit adders hooked together in ripple-carry fashion.
    2. Sixteen four-bit adders hooked together in ripple-carry fashion. Inside each of the four-bit adders, however, the carry lookahead is used.
    3. Four sixteen-bit adders hooked together in ripple-carry fashion. Each of the sixteen-bit adders is built as in option 3 of the prior exercise.
    4. Four sixteen-bit adders hooked together in carry lookahead fashion. As in the previous option, the sixteen-bit adders are built as in option 3 of the prior exercise.

Instructor: Max Hailperin