What is a Denary Number?
This question could also have been asked as What is the Denary Notation for a number? or What is the Denary Numerical System?
The Denary Notation is one of the five numerical notations discussed in Chapter 2 of Sir Roger Penrose's book The Emperor's New Mind. The other four notations are Unary, Binary, Expanded Binary, and Machine State. The last one is not so much a numerical notation as it is the Transition Function for a Turing Machine, but it can be converted to any one of the other notations, and for that reason it can also be thought of as a numerical notation.
A Denary number is the easiest one to explain! That's because we normally use the denary notation in our everyday conversations.
The Denary numbers are the following:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on.
My guess is that the British use the word Denary (rather than the equivalent word Decimal) much more frequently than Americans (like me) would do.
In his book The Emperor's New Mind, Sir Roger Penrose consistently used the word Denary. Since the main purpose of this website was to provide an Excel file that would allow the building and running of a Turing Machine according to the description in that book, I also used the word Denary when developing this website.
Of the five numerical notations, Denary numbers are the only ones that are of no direct use to the Penrose Turing Machine. They are meant only for human consumption.
The only reason you might want to translate a number to Denary from one of the other notations is to see what that number is in a notation that's familiar to you.
Version 1.0 -- April 23, 2017