Mixed Radix Number Representations

​
base-10 conventional representation
2257
constant radix
10
radix
0
10
radix
1
10
radix
2
10
radix
3
10
show radices
retain leading zeros
constant radix representation
mixed base representation
2257
2
10
2
10
5
10
7
10
In conventional positional notation systems, a numeral written as
d
3
d
2
d
1
d
0
has the value
{
d
3
,
d
2
,
d
1
,
d
0
}·{
3
b
,
2
b
,
1
b
,
0
b
}
where
b
is called the radix or base of the number system. The multipliers for each digit thus proceed from right to left in geometric sequence and each is a constant
b
multiplied by the multiplier of the digit to the right. This representation of numbers is often extremely convenient. There are instances, however, where it is useful to denote a numeric quantity where the ratio between the multiplier of a digit and the digit on its right is not necessarily a constant. Such representation systems are called mixed radix or mixed base number systems. This Demonstration shows how numbers represented in conventional positional notation systems can be represented as a mixed base form.

Details

Snapshot 1: the number 360 represented using the Mayan system in which all positions except the second have radix 20
Snapshot 2: the number 4095 represented in constant radix 2 and then represented using radices (from right to left) 16, 8, 4, 8
Snapshot 3: the number 2257 represented in constant radix 7
Snapshot 4: the Demonstration responds with an appropriate message if the number chosen is too large to be represented with the four mixed radix digits you selected

External Links

Gray Code (Wolfram MathWorld)
Mixed Base Gray Codes

Permanent Citation

Seth J. Chandler
​
​"Mixed Radix Number Representations"​
​http://demonstrations.wolfram.com/MixedRadixNumberRepresentations/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011