Can Turing Machine work with decimal numbers?

Question

I can do some operations on turing machine, but I use the binary forms of numbers, as the computers do. I wonder whether can I write decimal numbers on its tape and do calculation? Thanks in advance.

Of course you can. It all depends on your input alphabet. – clemens Sep 15 '17 at 12:54 — clemens, Sep 15 '17 at 12:54
Thank you macmoonshine, it was helpful. – igelr Sep 15 '17 at 12:56 — igelr, Sep 15 '17 at 12:56

score 1 · Accepted Answer · answered Sep 17 '17 at 20:59

Decimal numbers are strings of symbols. Thus they can be written on a TM tape and be manipulated in any computable way. This includes of course the normal arithmetic calculations.

Of course, you can only represent and manipulate decimal numbers with a finite number of significant digits (or one infinite one, but that does not seem useful). So in decimal, for example you cannot represent 1/3. If all rational numbers could occur, maybe the representation as fractions would be better, since it is always finite.

Can Turing Machine work with decimal numbers?

1 Answers1