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#1 2005-09-01 09:50:42

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

overflowing base-2 ?

Does anyone have a name for
a number system where the
digits can be values larger
than the base?  Here is an
example using base-2 places
but filling them with digits
up to 9.  Each four digit
number shown below has a
value of 68 in base-10.

8's  4's  2's  1's  place

7    3    0    0  roll

6    3    4    0  neutral

4    5    7    2  yikes

1    9    9    6  wink

8    1    0    0  lol

1    9    8    8  smile


igloo myrtilles fourmis

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#2 2005-09-01 17:04:55

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,963

Re: overflowing base-2 ?

I don't know what made you think of this idea. In base-n system, numbers greater than or equal to n are 'banned'.
Anyway, the illustration given by you was interesting. smile


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#3 2005-09-01 18:49:57

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: overflowing base-2 ?

Interesting concept. So they can't be called "base-n", but any mathematical concept is still valid of course. And there may even be a name for it that I don't know of.

In fact they can be expressed as polynomials:

7a³ +  3a² + 0a + 0
6a³ +  3a² + 4a + 0
etc..

Where a=2


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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