# MATH: Number Base Models

Ian Goddard (igoddard@erols.com)
Fri, 01 May 1998 12:32:47 -0400

Rather than this number-base model
(which some believe is proper):

B10 0 1 2 3 4 5 6 7 8 9
B9 0 1 2 3 4 5 6 7 8
B8 0 1 2 3 4 5 6 7
B7 0 1 2 3 4 5 6
B6 0 1 2 3 4 5
B5 0 1 2 3 4
B4 0 1 2 3
B3 0 1 2
B2 0 1
B1 0

which defines the Base 1 digit as 0 (thus
running the basic "tally-mark system" off the
road), would this not be a better Base n model?:

First,
notice that in B2 2 = 10
in B3 3 = 10
in B5 5 = 10
in B10 10 = 10

This means that in a system Bn, n correlates to
the carry of 1 to the next column to the left.
We could also say that in B1 1 = 10, since
the "0" is valueless. This defines what
might be an ideal number base model:

Number Base n (Bn) sytems:

B10 1 2 3 4 5 6 7 8 9 10
B9 1 2 3 4 5 6 7 8 10
B8 1 2 3 4 5 6 7 10
B7 1 2 3 4 5 6 10
B6 1 2 3 4 5 10
B5 1 2 3 4 10
B4 1 2 3 10
B3 1 2 10
B2 1 10
B1 10

Here, Base 1 is what it is, the
"tally-mark system," in which
every number in each column
has the value of just 1.

We could also define
Bn (n = frequency that
1 is carried to the column
to the left after number 1).

Ergo:

Base 1

1
11 carried 1
111 carried 1
1111 carried 1
11111 carried 1

Base 2

1
10 carried 1
11
100 carried 1
101
110 carried 1
111
1000 carried 1

Base 3

1
2
10 carried 1
11
12
100 carried 1
101
102
110 carried 1

Base 5

1
2
4
10 carried 1
11
12
13
14
20 carried 1

Base 10

1
2
3
4
5
6
7
8
9
10 carried 1
11
12
13
14
15
16
17
18
19
20 carried 1

Is this model and analysis logical?

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VISIT Ian Williams Goddard ----> http://www.erols.com/igoddard
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