Assignment 10, due Nov 4

On every assignment, write your name legibly as it appears on your University ID card! Homework is due on paper at the start of class on the day indicated (usually Friday). Exceptions will be made only by advance arrangement (excepting "acts of God"). Late work must be turned in to the TA's mailbox (ask the CS receptionist in 14 MLH for help). Never push homework under someone's door!

1. A Problem: What is the closest approximation to π (Pi, 3.14159...) as a 32-bit IEEE format floating point number? Give your answer in hexadecimal. You may use any tools you wish to find this value. (1.0 points).

2. Background: Consider this bizarrely minimal floating point format: Numbers are 4 bits long, 1 bit of sign, 2 bits of exponent, and 2 bits of mantissa, including a hidden bit. The exponent is expressed as a naturally biased binary number between -2 and 1, while the magnitude of the mantissa ranges from 1.0 to 1.5 (the point is immediately to the right of the hidden bit).

   A problem: Give a table of the decimal equivalents of every floating point number in this system from 0000 to 1111, in order. (1 point)

3. Background: Consider the following set of simultaneous boolean equations:
   • c = ad
   • d = b+c

   a) Draw this in the schematic notation for a logic circuit. (0.3 points)

   b) What values of the inputs to this circuit permit it to store one bit of information? (In doing part a, you will have identified the inputs.) (0.3 points)

   c) How do you make this circuit store the value one? (0.2 points)

   c) How do you make this circuit store the value zero? (0.2 points)