Assignment 11, due Nov 9

Always, on every assignment, please write your name legibly as it appears on your University ID and on the class list! All assignments will be due at the start of class on the day indicated (usually a Friday). The only exceptions to this rule will be by advance arrangement unless there is what insurance companies call "an act of God" - something outside your control. Homework must be turned in on paper and in class! Late work may be turned in to the teaching assistant's mailbox, but see the late work policy. Never push late work under someone's door!

Homework

1. Background: Consider this eccentric floating point format:

              _______________
             |_|_|_|_|_|_|_|_|
             |s|   e   |  m  |
   
              s = the sign of the mantissa
              e = the exponent, biased so that 1000 = 0
              m = the magnitude of the mantissa
   

   The mantissa magnitude is a 4-bit normalized positive binary fraction, such that 0.499 < m < 1; that is to say, there is a hidden bit. Assume that the definitions here are applied strictly, with no special cases! (1/5 point each)

   a) What is the decimal equivalent and the binary representation of the largest possible number in this format?

   b) What is the decimal equivalent and the binary representation of the smallest possible positive normalized nonzero number in this format?

   c) What is the decimal equivalent of 00000000 in this format?

   d) What is the decimal equivalent of 11111111 in this format?

   e) What is the binary representation of 1.0 in this format?

2. A problem: Fix the problems with the floating point add routine given in Chapter 11. This combines exercise r and s from that chapter. (1 point)

3. Background: Consider a logic circuit constructed as follows:

   x = a and y
   y = b or x (THE ORIGINAL HAD A TYPO HERE)

   a) Draw a schematic logic diagram for this circuit. (2/5 point)

   b) It is a flipflop. Therefore, it must be possible to set it, reset it, and make it remember. What combinations of values on the inputs do each of these. (3/5 point)