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Re: base 10 number system

Subject: Re: base 10 number system
From: "David T. Ashley"
Date: Sun, 31 Dec 2006 01:46:22 -0500
Newsgroups: sci.math
<bob@xxxxxxxxxxxxxx> wrote in message 
news:1167543213.802821.253360@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>I was just wondering why people tend to use a base 10 number system.  I
> can't help but wonder if it is due to us having ten fingers.  Anyone
> have any insight into this?

It is definitely due to having 10 fingers.

The reason for base-2 with computers is that it is easier to build an 
electronic circuit that is stable in two states rather than in a larger 
number of states.

See:

http://en.wikipedia.org/wiki/Flip-flop_(electronics)

Trust me, computers would have been base-10 if the underlying fabrication 
technology supported it.

Also, some of the early computers, I think, were base-10 in the sense that a 
lot of the instructions were geared towards base-10 operations (even though 
the underlying representation is base-2).  You find remnants of that even 
today with instructions like DAA (decimal adjust accumulator), etc.  I'm 
just guessing here (and I'm too lazy to look it up), but I suspect that 
existing floating point hardware supports BCD operations.

                                en.wikipedia.org/wiki/Binary-coded_decimal">http://en.wikipedia.org/wiki/Binary-coded_decimal

Other thoughts:

a)The prime factorization of 10 (2 * 5) means that a lot of common fractions 
(1/3 for example) can't be expressed exactly as decimal numbers.  I wonder 
if something like base 2 * 3 * 5 = 30 wouldn't be more logical.

b)It might not be fair with computers to say that they are base-2.  In some 
sense they are, but in another sense you might say they are base-256 (or 
larger).  For example, an inexpensive microcontroller can add two 8-bit 
numbers in a single instruction and get a 16-bit number (well, kind of, 
carry and all that).  Similarly for multiplication and division (in a sense, 
they have the base-256 addition, subtraction, etc. tables memorized in 
silicon).  I'm receptive to alternate opinions and ways of looking at that, 
however. 



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