I'm wondering if it is possible to represent a number as a sequence of bits, each having approximately the same significance, such that if we flip one of the bits, the overall value does not change by much.
For example, we can use sequences of 4-bits, where each group represents a value from 0 to 15 and the overall value is the sum of all these values.
0110 0101 1101 1010 1011 → 6 + 5 + 13 + 10 + 11 = 45
and now flipping any bit can only incur in a maximum difference of 8 in the final value.
Some drawbacks obviously exist with this approach:
- values have multiple representations, with some values having more representations than other ones (for example, there are 39280 distinct representations for the number 38, and only 1 for the number 0);
- the amount of values that can be represented is greatly reduced (this representation allows for integers from 0 to 75, while 20 bits could normally represent 220 ~ 1 million different integers).
Are there any resources I can find concerning this problem? I can't seem to find anything online, but maybe I'm not searching with the right keywords. What other alternatives exist to my approach? Do they improve on its disadvantages?