number from one scale into another is as follows: Multiply the first digit by the old radix in the new scale, and add the next digit; multiply the result again by the old radix in the new scale, and take in the next digit, and so on to the end, always using the radix of the scale you want to leave, and the notation of the scale you want to end in.
Thus, suppose it required to turn 16687 (duodecimal) into the decimal scale, and 16432 (septenary) into the quaternary scale:
| 16687 | 16432 |
|---|---|
| Duodecimals into Decimals. | Septenaries into Quaternaries. |
| 1 × 12 + 6 = 18 | 1 × 7 + 6 = 31 |
| × 12 + 6 | × 7 + 4 |
| 222 | 1133 |
| × 12 + 8 | × 7 + 3 |
| 2672 | 22130 |
| × 12 + 7 | × 7 + 2 |
| Answer 32071 | 1021012 |