Number Base Converter

One input per line. Output is numbered to match the input order.
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Understand Number Base Converter

Converts a whole number between binary, octal, decimal, and hexadecimal.

How it works

Every base is positional: each digit is multiplied by the base raised to its position. 0xFF is (15 × 16) + 15 = 255, and 11111111 in binary is the same value with eight ones. Hexadecimal earns its place in programming because the mapping to binary is exact — one hex digit is always four bits — so 0xFF is 11111111 and 0x0F is 00001111 with no arithmetic required. Octal groups bits in threes instead, which is why Unix permissions are octal: each digit is exactly one rwx triplet.

When to use it

  • Reading a bitmask or a set of flag constants out of firmware, a protocol spec, or a driver header
  • Translating a hex color channel to decimal, or an octal file mode to its binary bit pattern
  • Checking a memory address, register value, or byte offset shown in one base against documentation written in another
  • Working through a computer-science exercise where the conversion itself is the point

Watch out for

  • Prefixes are rejected. Enter `FF`, not `0xFF`, and `1010`, not `0b1010` — the `x` and `b` are not valid digits in their base and the input is refused.
  • Precision runs out above 2^53 − 1 (9,007,199,254,740,991). A 64-bit identifier, a Snowflake ID, or a full-width hash pasted as one number will convert to a rounded value that looks plausible and is wrong. Split it or use BigInt.
  • Negatives are shown in sign-magnitude form, so −5 becomes −101 in binary. That is not two's complement, which is what a CPU register actually holds (11111011 in eight bits).
  • Whole numbers only. There is no fractional part, so 0.5 cannot be shown as 0.1 in binary here.

Frequently Asked Questions

How do I convert hex to decimal?

Each hex digit represents a power of 16. 0xFF = (15×16) + 15 = 255. 0x1A = (1×16) + 10 = 26. The tool converts instantly — type in any base and all four representations update simultaneously.

Why is hexadecimal used in programming?

Hexadecimal maps cleanly to binary: one hex digit = exactly 4 bits. So 0xFF = 11111111 (all bits set), 0x0F = 00001111 (low 4 bits). This makes hex compact and readable for memory addresses, color values (#RRGGBB), bitmasks, and byte-level protocol fields.

What does octal represent in Unix permissions?

chmod 755 uses octal: 7 = 111 (rwx), 5 = 101 (r-x). The three octal digits map to owner, group, and other permissions. chmod 644 = 110 100 100 = rw-r--r--. Each of the three permission bits (read=4, write=2, execute=1) is a power of 2.

How to Use Number Base Converter

  1. Paste or type your input in the input area above.
  2. The tool processes your input automatically or click Run.
  3. Copy or download the result using the action buttons.
  4. Use Ctrl+Enter to run quickly from the keyboard.