Floating Points

About the music

Floating Points is the stage name of UK electronic producer Sam Shepherd. On top of being a musician, he is a neuroscientist with a PhD in neuroscience and epigenetics from University College London.

About the science

Floating points is a way to write a number often used in computers, with a fix number of significant digits scaled with a number at a certain exponent.

$$ 1.2345 = \underbrace{12345 * 10^{-4}}_{\text{floating point}}$$

We call the different numbers involved significand, base, exponent:

$$ \underbrace{12345}_{\text{significand}} * \underbrace{10}_{\text{base}}\!^{\overbrace{-4}^{\text{exponent}}}$$
  • significand: Number of significant digits, that builds up accuracy in the measure. They are the numbers that carry meaning, unlike leading zeros or sometimes trailing zeros …
  • base: Number exponentiated to scale the represented number. Should be an easy one for human like 10 or machine like 2 (binary) or 16 (hexadecimal).
  • exponent: Scale of the number

Fixed point representation would be to choose a number of digits after the (radix) point. For example with a fixed point of 2 we would write:

  • 123.45
  • 4444444.22
  • 1.23

Now why using one or the other ? In a computer, we want to minimize the space taken to stock a number. Thus if we decide to only give 7 digits to represent a number, using floating point allow us go until $ 999999*10^9 $ when fixed number with a radix of two digits can only go to $99999.99$.

Thus floating point allows a bigger span of number but for less precision than fixed point.