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Spring 06 CS61C Homework 5
==========================
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Floating and Fixed Point Numbers
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Update
------
* 2/28/06: In Question 2, treat the number as unsigned fixed number.
* 2/28/06: In Question 5, the input ``num`` can be negative.  The output type
           should therefore be ``int`` instead of ``unsigned``.  The code has
           been updated to reflect the change.

Corresponding Reading
---------------------
* P&H 3.5, Lecture Notes on Fixed Point Numbers

In this homeworkd, we use the notation ``fixed<w,b>`` to denote a
``w`` bits fixed point number with binary point at position ``b`` from
the least significant bit (counting from 0).  For example,
``fixed<32,3>`` denotes a 32-bit fixed point number, of which 3 right
most bits are fractional. 

Problems
--------

Question 1
~~~~~~~~~~
P&H Exercise 3.30.

Question 2
~~~~~~~~~~
What does the bit pattern from Question 1 represents for a ``fixed<32,3>``?

What does the bit pattern from Question 1 represents for a ``fixed<32,32>``?

What does the bit pattern from Question 1 represents for a ``fixed<32,0>``?

Question 3
~~~~~~~~~~
Show the IEEE-754 binary representation for the following decimal floating-point numbers:

	(a) 20.5
	(b) -2.625
	(c) 3 * 2\ :sup:`-145`
	(d) -0
	(e) +0

Question 4
~~~~~~~~~~
Show the binary representation for the following fixed-point
``fixed<8,3>`` numbers.  Truncate bits that are not representable.

	(a) 20.5\ :sub:`ten`
	(b) 2.33\ :sub:`ten`
	(c) 0.6875\ :sub:`ten`

OPTIONAL: What is the result if "even rounding" instead of truncation is used.

Question 5
~~~~~~~~~~
Complete the following C-function that converts a floating point
number ``num`` into a fixed point number of type ``fixed<32,bp>``.
You may truncate all bits that are not representable.: :: 

    int Float2Fixed(float num, int bp) {
        int result;

        /* your code goes here */

        return result;
    }

For example, ``Float2Fixed(5.5, 2)`` should return the
integer 22 with bit pattern: ::

    0000000000000000000000000000000000010110

Submission
----------
Your solution to Question 1 to 4 should be saved in a file
``hw5.txt``.  Your solution to Question 5 should be saved in a file
named ``hw5q5.c``.  From the directory that contains these two files, run: ::

     submit hw5