Floating Point Numbers

And my insights into them.

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Defining The Scope

This worklog was inspired by a mix of procrastination and my Numerical Analysis I class.
What do I mean by "Floating Point Numbers" in this case? The base-10 numbers with decimanl points?
No, this is about FP16, FP32, FP64 and so on, floating point numbers represented for computation.

Whats The Difference?

• These floating point numbers such as FP64 are numbers that are represented in $2^n$ (base-2) instead of $10^n$ (base-10)

• Computer recognized floating point types have defined bit allocation for their:

  Sign: $\pm$
  Exponent: $e2$
  Mantissa: $1.234\dots$

  In the case of FP64 this is 1-bit for the sign, 11-bits for the exponent, and 52-bits for the mantissa

• When computing floating point numbers, there are a number of factors to consider such as round-off error, ...