Assignment 1

 

            Reading Assignment:

Chapter 3.1 and 3.2 in Hennessy and Patterson.

Binary number section in Brown and Vranesic
 

  1. (9 points) For each part below devise a scheme to represent, in binary, each set of symbols
    1. Decimal Digits : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
    2. Alphabets : A, B, C, D, E, F
    3. Integers from 21 to 36
  2. (12 points) Suppose you want to represent positive integers in binary. Indicate how many bits are required to represent each of the following sets of integers:
    1. The integers from 0 to 127 inclusive
    2. The integers from 0 to 2,048 inclusive
    3. The integers from 0 to 32,500 inclusive
    4. The integers from 0 to 1,500,345 inclusive
  3. (9 points) Indicate how large a value can be represented by each of the binary quantities:
    1. 4-bits
    2. 12-bits
    3. 24-bits
  4. (15 points) Convert each of the following binary number into decimal. Assume these quantities represent unsigned integers.
    1. 1010
    2. 10010
    3. 0111110
    4. 10000000
    5. 0111111
  5. (15 points) Convert each of the following decimal numbers into binary.
    1. 6
    2. 13
    3. 111
    4. 147
    5. 511
  6. (10 points) Suppose you are a jogger who wants to use your ten fingers to count laps as you circle a track. How many laps can you conveniently count? Briefly justify your answer. (There is more than one possible answer here.)
  7. (10 points) Search on Google for Slide rule and explain its functioning in 5 lines or less.
  8. (20 points) Give a general formula to compute time it takes to compute an nth order polynomial (where the highest power of x is n) using the two different computing structure given in your notes. Assume that a multiplier take time tm and an adder take times ta.