Convert Duodecimal (Base 12) to Binary (Base 2) with step-by-step solution.
0123456789ABEach digit × 12^position:
| Digit | Value | Position | Calculation | Result |
|---|---|---|---|---|
| 2 | 2 | 2 | 2 × 12^2 | 288 |
| 5 | 5 | 1 | 5 × 12^1 | 60 |
| 5 | 5 | 0 | 5 × 12^0 | 5 |
Divide by 2, collect remainders:
| Step | Dividend | ÷ 2 | Quotient | Remainder | Digit |
|---|---|---|---|---|---|
| 1 | 353 | ÷ 2 | 176 | 1 | 1 |
| 2 | 176 | ÷ 2 | 88 | 0 | 0 |
| 3 | 88 | ÷ 2 | 44 | 0 | 0 |
| 4 | 44 | ÷ 2 | 22 | 0 | 0 |
| 5 | 22 | ÷ 2 | 11 | 0 | 0 |
| 6 | 11 | ÷ 2 | 5 | 1 | 1 |
| 7 | 5 | ÷ 2 | 2 | 1 | 1 |
| 8 | 2 | ÷ 2 | 1 | 0 | 0 |
| 9 | 1 | ÷ 2 | 0 | 1 | 1 |
| Decimal | Duodecimal | Binary |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 | 10 |
| 3 | 3 | 11 |
| 4 | 4 | 100 |
| 5 | 5 | 101 |
| 6 | 6 | 110 |
| 7 | 7 | 111 |
| 8 | 8 | 1000 |
| 9 | 9 | 1001 |
| 10 | A | 1010 |
| 15 | 13 | 1111 |
| 16 | 14 | 10000 |
| 20 | 18 | 10100 |
| 32 | 28 | 100000 |
| Number System | Base | Value |
|---|---|---|
| Binary | 2 | 101100001 |
| Octal | 8 | 541 |
| Decimal | 10 | 353 |
| Hexadecimal | 16 | 161 |
| Ternary | 3 | 111002 |
| Quaternary | 4 | 11201 |
| Quinary | 5 | 2403 |
| Senary | 6 | 1345 |
| Septenary | 7 | 1013 |
| Vigesimal | 20 | HD |
| Duotrigesimal | 32 | B1 |
| Hexatrigesimal | 36 | 9T |
To convert from Duodecimal (base 12) to Binary (base 2), first convert to decimal, then convert from decimal to Binary.
Dozen system, highly divisible. Uses digits: 0123456789AB
Used in computers and digital systems. Uses digits: 01