CSC152 2006S, Class 10: Binary Representation

Admin:
* Syllabus rearranged
* No programming homework for tomorrow
* Reading: Conditionals in Java (ready later today)
* Don't worry about understanding all of Javadoc; just be able to extract key methods

Overview:
* Numbers wrapup
* About binary representation
* Lab

Numbers: 

* Questions?
  * Tell us more about doubles and Doubles and the ilk
    * In "normal math": integer and real (can have fractional part)
    * In computers, various kinds of integers and reals
      * Integers: int, short, long, byte
      * Reals: double, float
    * Generally a fixed number of bits.
      * IN Java, 32 for int, 16 for short, 8 for byte, 64 for long
      * For reals, something like 32 for float and 64 for double
    * The limited number of bits means that we don't represent
      most reals exactly; we simply approximate
  * Tell us more about the crappy problem you wrote with both doubles and floats
    * By default, if you write something that looks like a real, Java assumes you mean a double
        3.1, "ah hah, that's a double"
    * Doubles are more accurate than floats, so Java is loathe to treat a double as a float.  (The reverse is not true.)
    * Math.sqrt returns a double
    * When you tried to treat the return value as a float, Java got upset.
    * Solution
        float f;
        f = (float) Math.sqrt(2.0);
  * So why did you write that crappy problem?
    * I'm an idito.
  * Why use floats if doubles are more accurate?
    * Sometimes people care a lot about their memory usage, and don't need the accuracy
    * Not an issue in this class.  Use double.
  * How do we read integers?
    * Read a string
    * Use Integer.parseInt to convert the string to an int
        String in;
        pen.print("Please enter a number: ");
        pen.flush();
        in = eyes.readLine();
        int userinput;
        userinput = Integer.parseInt(in);
    * Similarly
        pen.print("Please enter a number: "); pen.flush();
        int userinput = Integer.parseInt(eyes.readLine());

Important lessons
* When you exceed the largest int (long, short, etc.) value,
  you have unclear results.
* When you exceed the largest double, you get "infinity"
* Reading numeric input (see above)

Back to questions:
* How do you include the factional component?
  * Use num.remainder(divisor); (from BigInteger)

Binary Representation
* Is it really the case that all of the other representations don't get quite the right answer in at least one case?
  * Yes.  That's why most computer scientists like two's complement.
* Can you explain inverting in two's complement?
  * Think about it as a "process" issue: Make a positive number negative or a negative number positive.
  * Two's complement: Two-step negation process: Flip the bits, add 1
* How do you tell whether a number is positive or negative?
  * The leading bit tells you.  If it's 0, the number is positive (or 0), if it's 1, the number is negative.