Math Is Fun Forum

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 

6    3    4    0 

4    5    7    2 

1    9    9    6 

8    1    0    0 

1    9    8    8 

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igloo myrtilles fourmis

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 52,350

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.

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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.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

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

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