13 in Binary
13 in binary is 1101. It takes 4 bits to write, and as a full byte it is 00001101.
How to convert 13 to binary
Divide by 2, write down the remainder, and repeat with the quotient until it reaches 0. The remainders, read from the last row up to the first, spell out 1101.
| Division | Quotient | Remainder |
|---|---|---|
| 13 ÷ 2 | 6 | 1 |
| 6 ÷ 2 | 3 | 0 |
| 3 ÷ 2 | 1 | 1 |
| 1 ÷ 2 | 0 | 1 |
Check it the other way
To verify, read 1101 left to right, giving each digit its place value and adding up the places that hold a 1.
| Bit | Place value | Contributes |
|---|---|---|
| 1 | 23 = 8 | 8 |
| 1 | 22 = 4 | 4 |
| 0 | 21 = 2 | 0 |
| 1 | 20 = 1 | 1 |
Adding the contributions: 8 + 4 + 0 + 1 = 13. The conversion checks out.
13 in every base
| Format | Value |
|---|---|
| Binary | 1101 |
| Decimal | 13 |
| Hexadecimal | D |
| Octal | 15 |
| As a byte (8-bit) | 00001101 |
Worth knowing about 13
Thirteen carries enough cultural baggage to have its own phobia name, triskaidekaphobia, yet in binary it is a tidy 1101: 8 plus 4 plus 1.
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FAQ
What is 13 in binary?
In binary, 13 is written 1101. That is 4 digits, each one a power of two: the pattern says which of 1, 2, 4, 8, and so on to add together to make 13. Computers store it as the byte 00001101, padding the front with zeros.
How many bits does 13 need?
It takes 4 bits to write 13 in binary, since 1101 has 4 digits and dropping any of them would change the value. Real hardware rounds up to whole bytes, so 13 normally sits in eight bits as 00001101, with the unused positions set to zero.
What is 13 in hex?
In hex, 13 is written D. Because 16 is a power of two, hex lines up neatly with binary: one hex digit always covers four bits, so 1101 compresses cleanly. The octal form, common in file permissions, is 15. Same number, three different notations.