..  _hw3-computer-math:

Homework 3: Computer Math
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Of course computers can do math. But exactly how computers do math is a bit of
a surprise to beginning programmers. Computer math is not exactly like the math
you have been learning all this time. We need to play with it a bit and see
why.

Integers
********

One basic kind of number used in computers is an "integer". This is a simple
one, it has no fractional part, and no decimal point (or commas for that
matter):

    * 1,3,5,-7, 11 are all integers

Integer Operations
==================

    * Adding, subtracting and multiplication all act normally.

    * Division is different!

        * remember how you did this in elementary school!

    * What is 5 / 2?

        * Not 2.5, tht is a different number

        * 2 goes into 5 2 times (with a remainder of 1)

        * You learned this long ago, but probably forgot it.

    * Limits
        
        * From HW2, you say the range of legal numbers for some "types" of numbers in C++

        * What happens if you go beyond those values.

            * unsigned number is 0, what is one less than that?

            * unsigned number is limited to 255, what is one more than that?

Floating Point Numbers
**********************

"Real" numbers have decimal points, and fractional parts. They can be very big,
or very little.

    * Two different ways of showing them:

        * Fixed point: 4.5
    
        * Scientific: 0.45E+01
        
            * The "Enn" part adjusts the decimal point by some power of 10)

        * Not every number can be represented: 1.0/3.0

            * The "errors" in numbers can be a problem in some calculations:
              1.0 / 3.0 * 3.0 = 0.99999999999

What to do
**********

As part of learning about computer arithmetic, let's explore some basic terms.
o a bit of research into computer arithmetic. Specifically see what you can find out
about these terms:

    * Arithmetic Overflow

    * Arithmetic Underflow

    * IEEE Floating Point

    * Double Precision

    * Sign Bit

    * Rounding/Truncation

    * Arbitrary Precision

    * Precedence Rules

write a short paragraph describing what each of these terms is about. Submit
that text file on BB.