Floating Point Properties

We have seen how to represent floating point numbers, as well as how to conduct basic operations with them. Now let’s explore the properties of our representation.

Precision

Precision intrinsically has to do with significant figures. In layman’s terms, these are how many digits we have available to us. This is especially relevant when we’re designing number representations for computers because we only have a fixed amount of space we can give each number.

So, how precise can we get with our $8$-bit floating point representation? Our precision is entirely dependent on where we are on the number line.

For example, say we have the number $3.5$, and we want to find out the smallest amount we can add to it without getting an overflow. This is essentially the precision at exponent $1$ ($1$ is the exponent when we write $3.5$ in floating point notation).

To find the precision at any floating point exponent we follow these steps:

• Find out how big the window between the current exponent and the next one is. For this case, we find $2^2-2^1$

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