WOLFRAM|DEMONSTRATIONS PROJECT

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.