# Number and character representation within computers

### March 2010

### what's a number?

How is a number (quantity) represented, stored in memory, or sent via some communications protocol? There is no "real" or "right" way. When you have the concept in your head of "one hundred and twenty three", how you express that is utterly independent from the concept. Arabic or roman digits, 123 small stones, etc. The concept of a quantity is utterly independent of it's representation.

The serial port (or USB port; the "S" means Serial) on the desktop/laptop and microcontrollers like the Arduino sends eight 1-bit digits at a time, asynchronously, eg. "at any time" not synchronized with anything external (like time of day, whatever). Please see my Bits, Baud, Modulation Rates" on how that works, and for true priests of the order, read Danny Cohen's On Holy Wars, or a Plea for Peace on how *bits* are sent.

With 8 contiguous one-bit states you can ENCODE a decimal number 0 to 255, a binary number 00000000 to 11111111, a hexadecimal number 00 to ff, etc. We call that conventionally a byte. You know I hope that 123 decimal is the same as 7B in hexadecimal notation, same as 01111011 in base two notation, and is a *representation* of the number of objects in a jar. It is not the objects in the jar.

With only byte-sized numbers, how do you represent 1234? Well one obvious way is to use different sized representations, like 16 or 32 bits, and this is of course commonly done. But it is impractical and unwieldy and not taking advantage of our convenient machinery to keep making up ad hoc representations for all possible datums.