13 in binary is 1101. The decimal number 13 converts to binary 1101₂ using repeated division by 2. In 8-bit form: 00001101. The page shows the full step-by-step division table, an 8-bit visualiser with place values, and conversions to octal (15) and hexadecimal (D)....
13 IN BINARY (BASE 2)
1101
13₁₀ = 1101₂
Binary (base 2)
1101
8-bit binary
00001101
Octal (base 8)
15
Hex (base 16)
D
Bit length
4 bits
Active bits (1s)
3 of 4
Even or odd?
Odd (ends in 1)
Power of 2?
No
STEP-BY-STEP — REPEATED DIVISION BY 2
| Dividend | ÷ 2 | Quotient | Remainder ↑ |
|---|---|---|---|
| 13 | ÷ 2 | 6 | 1 |
| 6 | ÷ 2 | 3 | 0 |
| 3 | ÷ 2 | 1 | 1 |
| 1 | ÷ 2 | 0 | 1 |
Read remainders from bottom to top: 1101 = 1101
FUN FACT
13 in binary is 1101. 13 is prime. 13 = 8 + 4 + 1 = 2^3 + 2^2 + 2^0, so the second bit from the right is 0.
8-BIT REPRESENTATION
2⁷
128
2⁶
64
2⁵
32
2⁴
16
2³
8
2²
4
2¹
2
2⁰
1
3 active bits — 2³ + 2² + 2² = 13
PLACE VALUE BREAKDOWN
| 2³ | 2² | 2¹ | 2⁰ |
|---|---|---|---|
| 8 | 4 | 2 | 1 |
| 1 | 1 | 0 | 1 |
8 + 4 + 1 = 13 ✓
BASE CONVERSIONS
Decimal (base 10)
Standard counting system
13
Binary (base 2)
Used in all digital computing
1101
Octal (base 8)
Used in Unix permissions
15
Hexadecimal (16)
Used in colours, memory addresses
D
DECIMAL 0–30 IN BINARY
Write down the decimal number 13. To convert to binary, repeatedly divide by 2 and record the remainder at each step.
13 ÷ 2 = 6 remainder 1 6 ÷ 2 = 3 remainder 0 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Read remainders bottom to top: 1101
Read the remainders from bottom to top: 1101. This is the binary representation of 13.
Verify by converting back: 1 + 4 + 8 = 13. ✓
13 to binary: 13 ÷ 2 = 6 remainder 1 6 ÷ 2 = 3 remainder 0 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Read remainders bottom to top: 1101 13₁₀ = 1101₂ 8-bit: 00001101 Octal: 15 Hex: D
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Last updated: April 29, 2026 · Verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.