Convert Duotrigesimal (Base 32) to Septenary (Base 7) with step-by-step solution.
0123456789ABCDEFGHIJKLMNOPQRSTUVEach digit × 32^position:
| Digit | Value | Position | Calculation | Result |
|---|---|---|---|---|
| 2 | 2 | 2 | 2 × 32^2 | 2,048 |
| 5 | 5 | 1 | 5 × 32^1 | 160 |
| 5 | 5 | 0 | 5 × 32^0 | 5 |
Divide by 7, collect remainders:
| Step | Dividend | ÷ 7 | Quotient | Remainder | Digit |
|---|---|---|---|---|---|
| 1 | 2213 | ÷ 7 | 316 | 1 | 1 |
| 2 | 316 | ÷ 7 | 45 | 1 | 1 |
| 3 | 45 | ÷ 7 | 6 | 3 | 3 |
| 4 | 6 | ÷ 7 | 0 | 6 | 6 |
| Decimal | Duotrigesimal | Septenary |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 3 | 3 | 3 |
| 4 | 4 | 4 |
| 5 | 5 | 5 |
| 6 | 6 | 6 |
| 7 | 7 | 10 |
| 8 | 8 | 11 |
| 9 | 9 | 12 |
| 10 | A | 13 |
| 15 | F | 21 |
| 16 | G | 22 |
| 20 | K | 26 |
| 32 | 10 | 44 |
| Number System | Base | Value |
|---|---|---|
| Binary | 2 | 100010100101 |
| Octal | 8 | 4245 |
| Decimal | 10 | 2213 |
| Hexadecimal | 16 | 8A5 |
| Ternary | 3 | 10000222 |
| Quaternary | 4 | 202211 |
| Quinary | 5 | 32323 |
| Senary | 6 | 14125 |
| Septenary | 7 | 6311 |
| Duodecimal | 12 | 1345 |
| Vigesimal | 20 | 5AD |
| Hexatrigesimal | 36 | 1PH |
To convert from Duotrigesimal (base 32) to Septenary (base 7), first convert to decimal, then convert from decimal to Septenary.
Used in encoding schemes. Uses digits: 0123456789ABCDEFGHIJKLMNOPQRSTUV
Days of the week. Uses digits: 0123456