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