Re: tone wheel or electronics ?

[ap748@freenet.carleton.ca (Mike Sues)]

>
>                   Can this be done digitally - hard to divide a number by 
>   5 or 3 ect. and not have a remainder (beat).
>
>Nah; it's trivial.
>
>  -- Don

Hah ! ... never thought I'd get into any mathematics here but ... the point is
that in the digital world, sure you can divide numbers (every computer does
it !) but there is an error. When representing the numbers in computers we
have to pre-define a length for the number's representation. If the result of
an operation cannot be fully "fit" into this representation then a 
"truncation error" occurs ... that is, the result is not the EXACT 
representation of a number ... hence in a divide operation this yields a
remainder. This is especially prevelant in certain types of numbers for which
only an infinite number of bits suffices to represent it ... the example
5/3 is perfect for this as 5/3 = 1 and 1/3 = 1.333 .... and so on ... other
classes of numbers, called the transcendentals (can never spell that darn
thing !) which are represented by an infinite, non-repeating sequence of
integers in 0-9 .. pi and e (natural log) are examples of this.

Hmm ... my numerical analysis is a bit rusty so the "truncation error" may
actually be referred to as a "rounding error" ... anyways you get the idea.


--
Mike
<ap748@freenet.carleton.ca>
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