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|---|---|
| HEX | — |
| BIN | — |
| OCT | — |
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Bin, Oct, Dec, Hex — live umrechnen, während Sie tippen.
| DEC | — |
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| HEX | — |
| BIN | — |
| OCT | — |
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Hexadecimal is the language of hardware. Binary is the foundation of every digital system.
Live conversion between Bin, Oct, Dec, and Hex.
Hexadecimal numbers (base 16) are the bridge between human and machine. Two hex digits = one byte — hence the standard for memory addresses, color codes, MAC addresses, and binary dumps. 0x7F is more readable than 01111111, but just as precise.
Every computer works with binary numbers (base 2). Subnet masks, bitmasks, GPIO pins: everything at the bit level. Our converter displays binary values with 4-bit grouping — 11111111 becomes 1111 1111.
Octal numbers (base 8) are Unix DNA: file permissions (chmod 755), character escapes (\033). Three bits per octal digit — the most compact human-readable format for short binary values.
Select the source format, type a number — all three other formats appear instantly. Ideal for debugging, embedded development, and CCNA exams.
The first 16 values are the multiplication table of number systems. Once you know them by heart, binary dumps and memory addresses read much faster:
| Decimal | Hex | Binary | Octal |
|---|---|---|---|
| 0 | 0 | 0000 | 0 |
| 1 | 1 | 0001 | 1 |
| 2 | 2 | 0010 | 2 |
| 3 | 3 | 0011 | 3 |
| 4 | 4 | 0100 | 4 |
| 5 | 5 | 0101 | 5 |
| 6 | 6 | 0110 | 6 |
| 7 | 7 | 0111 | 7 |
| 8 | 8 | 1000 | 10 |
| 9 | 9 | 1001 | 11 |
| 10 | A | 1010 | 12 |
| 11 | B | 1011 | 13 |
| 12 | C | 1100 | 14 |
| 13 | D | 1101 | 15 |
| 14 | E | 1110 | 16 |
| 15 | F | 1111 | 17 |
Pattern: each hex digit maps to exactly four bits. So 0x2F becomes 0010 1111 — no arithmetic, just look up the four bits per digit.
In practice you rarely see only positive values. Processors store negative numbers in two's complement: the highest bit is the sign, and a negative value is formed by inverting all bits and adding 1.
In 8 bits: -1 is 0xFF, i.e. 1111 1111. -2 is 0xFE. That is why logs or ss output sometimes show -1 where you expected 255 — same bits, different interpretation.
When widening, sign extension applies: a negative 8-bit value is padded with the sign bit up to 32 bits. 0xFF becomes 0xFFFFFFFF, not 0x000000FF. This is where classic off-by-256 bugs come from.
Whether a value fits depends on the bit width. Keep these limits in mind:
| Bits | unsigned (max) | signed (max) |
|---|---|---|
| 8 | 255 | 127 |
| 16 | 65535 | 32767 |
| 32 | 4294967295 | 2147483647 |
| 64 | 18446744073709551615 | 9223372036854775807 |
You meet these limits everywhere: a byte (8 bit) holds 0 to 255, a TCP or UDP port is 16 bit (0 to 65535), an IPv4 address is 32 bit, and modern counters or filesystem values are often 64 bit. Enter 256 as a port number and you get no error message — just a wrong result.
0755 is octal, i.e. 493 decimal. In Python 3 and in this converter a leading zero is invalid. If you mean permissions, verify the result.FF without 0x is not a number but text. This converter accepts both — scripts and APIs usually do not.0xFF is 255 (unsigned) or -1 (8 bit, two's complement). Both are correct — context decides.0010 and 10 are the same value (2). Leading zeros only show the bit width — useful for reading, no effect on the value.Three everyday IT situations: You want to convert a MAC address like 00:1A:2B:3C:4D:5E to binary to explain an access list problem. You stumble over a color like 0xFF8800 and want to know which RGB values hide behind it. Or you want to finally explain to a colleague why chmod 755 grants exactly those permissions. This converter is here for all of that — and it calculates live.
Choose the source format — for example Decimal (DEC) for a number you just read from a log.
Type the number. The converter also understands the 0x prefix for hexadecimal values.
All other formats appear instantly — no convert button needed. Example: 255 becomes 0xFF and 11111111.
The color 0xFF8800 splits into three bytes: FF = 255 (red), 88 = 136 (green), 00 = 0 (blue) — a strong orange. Since each digit pair is exactly one byte, a 6-digit hex color always consists of three RGB components. Type it into the converter — it breaks it down into decimal and binary live.
One hex digit covers 16 values (0–9, A–F), two digits therefore 16 × 16 = 256 values — exactly one byte. That's why FF = 255 maps perfectly onto the maximum value of a byte. This 1:1 relationship makes hex the shorthand for binary: a MAC address like 00:1A:2B is the compact form of 48 bits, and IPv6 addresses are 128 bits in hex groups.
Octal (base 8) looks exotic today but is deeply rooted in Unix: chmod 755 splits into three digits of 3 bits each: read (4), write (2), execute (1) adds up to 7. Character escapes like \033 for ESC in shell scripts are octal too — three bits per digit make octal the most compact human-readable representation for 6- or 9-bit values.
Because two hex digits are exactly one byte. You write 255 instead of 11111111 — fewer digits, fewer reading errors, and each digit pair corresponds directly to a byte in memory.
0xFF is hexadecimal for 255 — the maximum value of a byte, with all 8 bits set. In CSS that's the color white, in subnet masks the familiar 255.
Fastest with this converter: set the format to decimal, type the number, read the binary value. To understand it: repeatedly divide the number by 2 and note the remainders from bottom to top.
Both map the same number space, just with different digits: binary only knows 0 and 1, hex uses 0–9 plus A–F. The value is identical — the notation is just shorter: 11111111 = FF.
More on number systems in our blog: Zahlenwelten des Admins. IP ranges? The subnet calculator handles them — a feel for binary helps there too.