Conversor de zonas horarias

What a number base actually is

A number base — or radix — is simply how many distinct digits a system uses before it rolls over to the next place. We count in base 10 because we have ten fingers, so after 9 we add a new column and write 10. Computers count in base 2 (binary) because a transistor is either on or off, giving just two digits, 0 and 1. The value of a written number does not change between bases; only its representation does. The decimal number 255, the binary 11111111, the octal 377, and the hexadecimal FF all describe the exact same quantity. This converter shows all four at once and updates every field the instant you type in any of them.

The positional formula

Every base works the same way: each digit is multiplied by the base raised to the power of its position, counting from zero on the right. To read binary 1011 in decimal you compute 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11. The same rule converts any base. Hexadecimal 2F is 2×16¹ + 15×16⁰ = 32 + 15 = 47, where the letter F stands for the digit fifteen. Hex uses A–F precisely because base 16 needs sixteen single-character digits and we run out of 0–9 after ten.

The four common bases

Hex is popular in computing because each hex digit maps cleanly onto exactly four binary bits. The byte 11010110 splits into 1101 and 0110, which are D and 6, so the whole byte is D6 — far easier to read and type than eight ones and zeros.

A worked example with the bit breakdown

Type 255 in the decimal field (the tool starts with this value). Instantly the binary shows 11111111, octal 377, and hex FF. Below, the 32-bit breakdown pads the binary out to a full word: 00000000 00000000 00000000 11111111, grouped in fours with alternating colors so you can count places at a glance. The line beneath confirms the value as both unsigned and signed. Now type a hex like FF in its own field instead — every other field updates the same way, because the tool converts whatever you enter back to decimal and re-derives the rest.

The 32-bit limit you must know about

This converter operates on 32-bit integers. Internally it treats your value with an unsigned 32-bit conversion, so the working range is 0 to 4,294,967,295 (hex FFFFFFFF). The breakdown line also shows the signed interpretation: in two's-complement, values from 0x80000000 upward read as negative, which is why a large positive decimal can show a negative "signed 32-bit" figure. This mirrors exactly how a 32-bit CPU register behaves, but it means the tool is not intended for arbitrarily huge numbers — those exceed a single 32-bit word.

Custom bases from 2 to 36

Beyond the four standard fields, the custom-base box converts to any radix from 2 to 36. Why 36? After the ten digits 0–9 you can use the 26 letters A–Z as extra digits, and 10 + 26 = 36. Base 36 is sometimes used to shorten numeric IDs into compact alphanumeric strings. Set the base to 36 and enter a decimal, and a long number collapses into a handful of characters.

Practical use cases

• Decoding hex color codes. A CSS color like #FF6B35 is three hex bytes; convert each pair to decimal to get the red, green, and blue channel values.
• Reading file permissions. Unix chmod 755 is octal; convert to binary to see the read/write/execute bits.
• Inspecting bitmasks and flags. The 32-bit breakdown shows exactly which bits are set in a flags value.
• Working with memory addresses printed in hex by debuggers and crash logs.

Common mistakes

• Including the prefix. Enter FF, not 0xFF, in the hex field, and 11111111, not 0b11111111, in binary. The prefixes mark a literal in code but are not part of the digits.
• Using invalid digits. A 2 in a binary field or a G in a hex field is not a valid digit for that base and will not convert.
• Expecting fractions. This tool converts integers; binary and hex fractional points are a separate topic.

Privacy

All conversion is arithmetic performed in your browser with no network calls. Nothing you type is uploaded or stored, and the tool works fully offline.