From a tee-shirt:

One of the members here had that in his/her signature for a long time.

There are two kinds of binary states : the memory cell is either half full or half empty.

There are two kinds of people. Those who don't understand binary say that binary is very exact, since it is either one or zero. Those who understand binary know that is not true, because floating point numbers are almost never exact.

so you need to be "brainy" to understand "binary"?

Koepel:

... floating pointer numbers are almost never exact.

Or is it that floating point numbers are exact; it is the human readable representation that fails

I think it is the floating pins that make it hard for the processor to understand binary. People are 0 until they figure out that lesson, and then they are 1

Koepel:

because floating point numbers are almost never exact.

A floating point number is always exact, but it is not always exactly equal to the number it approximates.

For example, the nearest IEEE754 single-precision approximation to pi is *exactly* 3.1415927410125732421875, which is not exactly equal to pi (it's correct up to 7 decimal digits).