Convert Septenary (Base 7) to Binary (Base 2) with step-by-step solution.
0123456Each digit × 7^position:
| Digit | Value | Position | Calculation | Result |
|---|---|---|---|---|
| 2 | 2 | 2 | 2 × 7^2 | 98 |
| 5 | 5 | 1 | 5 × 7^1 | 35 |
| 5 | 5 | 0 | 5 × 7^0 | 5 |
Divide by 2, collect remainders:
| Step | Dividend | ÷ 2 | Quotient | Remainder | Digit |
|---|---|---|---|---|---|
| 1 | 138 | ÷ 2 | 69 | 0 | 0 |
| 2 | 69 | ÷ 2 | 34 | 1 | 1 |
| 3 | 34 | ÷ 2 | 17 | 0 | 0 |
| 4 | 17 | ÷ 2 | 8 | 1 | 1 |
| 5 | 8 | ÷ 2 | 4 | 0 | 0 |
| 6 | 4 | ÷ 2 | 2 | 0 | 0 |
| 7 | 2 | ÷ 2 | 1 | 0 | 0 |
| 8 | 1 | ÷ 2 | 0 | 1 | 1 |
| Decimal | Septenary | Binary |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 | 10 |
| 3 | 3 | 11 |
| 4 | 4 | 100 |
| 5 | 5 | 101 |
| 6 | 6 | 110 |
| 7 | 10 | 111 |
| 8 | 11 | 1000 |
| 9 | 12 | 1001 |
| 10 | 13 | 1010 |
| 15 | 21 | 1111 |
| 16 | 22 | 10000 |
| 20 | 26 | 10100 |
| 32 | 44 | 100000 |
| Number System | Base | Value |
|---|---|---|
| Binary | 2 | 10001010 |
| Octal | 8 | 212 |
| Decimal | 10 | 138 |
| Hexadecimal | 16 | 8A |
| Ternary | 3 | 12010 |
| Quaternary | 4 | 2022 |
| Quinary | 5 | 1023 |
| Senary | 6 | 350 |
| Duodecimal | 12 | B6 |
| Vigesimal | 20 | 6I |
| Duotrigesimal | 32 | 4A |
| Hexatrigesimal | 36 | 3U |
To convert from Septenary (base 7) to Binary (base 2), first convert to decimal, then convert from decimal to Binary.
Days of the week. Uses digits: 0123456
Used in computers and digital systems. Uses digits: 01