Number Bases
Place value in any base
Each digit is multiplied by the base raised to its column index, counting from zero at the right.
The Formula
value = d(n-1) x b^(n-1) + ... + d1 x b^1 + d0 x b^0
Each digit is multiplied by the base raised to its column index, counting from zero at the right.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| d_i | Digit | digit | The digit in column i, from zero to base minus one. |
| b | Base | radix | How many digits the system uses. |
| i | Position | index | Column index, zero at the rightmost digit. |
What Each Symbol Means
d_idigit
Digit
The digit in column i, from zero to base minus one.
bradix
Base
How many digits the system uses.
iindex
Position
Column index, zero at the rightmost digit.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to convert number bases page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Convert Number Bases, filed under Unit Conversion. Every number the guide produces comes from substituting into this one line.