n-digit

An \(n\)-digit is a phys­i­cal ob­ject that can be sta­bly placed into any of \(n\) dis­t­in­guish­able states. For ex­am­ple, a coin (which can be placed heads or tails) and a sin­gle bit of mem­ory on a com­puter (which ei­ther has a high volt level or a low volt level) are both ex­am­ples of 2-digits. A digit wheel is an ex­am­ple of a 10-digit. One die is an ex­am­ple of a 6-digit; two dice to­gether are an ex­am­ple of a 36-digit (be­cause they can be placed in 36 differ­ent ways).

What does and doesn’t count as an \(n\)-digit de­pends on con­text and con­ven­tion: For ex­am­ple, if you want to com­mu­ni­cate a mes­sage to me by plac­ing a penny heads-side up and choos­ing whether to point Abra­ham Lin­coln’s face ei­ther north, south, east, or west, then, for the pur­poses of the two of us, that penny is a 4-digit rather than a 2-digit. The defi­ni­tion of “sta­bly placed” is also a bit up-for-grabs: If you’re writ­ing a com­puter pro­gram and need to store a 256-mes­sage in short-term mem­ory, then a byte of RAM will do, but if you need to store the same 256-mes­sage for a long pe­riod of time, you may need to use a less tem­po­rary 256-digit (such as a hard drive).

Note that it’s pos­si­ble to em­u­late \(m\)-digits us­ing \(n\)-digits, in gen­eral. If \(m < n\) then an \(n\)-digit is triv­ially an \(m\)-digit (i.e., you can use a digit wheel like a 7-digit in a pinch), and if \(m > n\) then, given enough \(n\)-digits, you can make do. For ex­am­ple, 3 coins can be used to en­code an 8-digit. See also em­u­lat­ing digits.

Parents:

  • Mathematics

    Math­e­mat­ics is the study of num­bers and other ideal ob­jects that can be de­scribed by ax­ioms.