Floating point: arithmetic

Addition of floating point numbers requires some adjustment if the exponents are not the same.

Base 10:

3.2 * 102 + 4.3 * 104

.032 * 104 + 4.3 * 104

4.3032 * 104

Does it matter which way we adjust?

IEEE754:

1. Convert to scientific notation

2. Shift radix point so exponents are the same (which way?)

3. Add 2 mantissas (or subtract if different signs)

4. If sum does not have a single 1 bit to the left of the radix point, shift and adjust exponent

5. Determine sign

6. Convert back to floating point representation

Multiplication actually requires less adjustment:

1. Multiply mantissas

2. Add exponents

3. Determine sign

4. Re-normalize