Number Base Converter

About the Number Base Converter

Computers store everything as patterns of on and off, but people read numbers in tens, so moving between bases is a daily chore for anyone near code, networks, or electronics. This converter shows one whole number in four positional systems at once: binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Type into any of the four fields and the other three redraw instantly, so you can start from whichever form you have in front of you, such as a hex color or a file permission, and read off the rest.

All four systems work the same way: each digit is multiplied by the base raised to the digit's position, counted from zero at the right, and the products are added. Decimal 493 is 4x100 + 9x10 + 3x1, and binary 111101101 is 1x256 + 1x128 + 1x64 + 1x32 + 0x16 + 1x8 + 1x4 + 0x2 + 1x1, which also equals 493. The bases that are powers of two are popular because they line up with bits: one hex digit is exactly four bits, so a byte is always two hex digits, and one octal digit is exactly three bits.

Students use it to check homework, web developers to read color codes, system administrators to decode Unix file permissions, and electronics hobbyists to interpret register values or addresses. The tool deals only in non-negative whole numbers up to JavaScript's safe-integer limit of 9,007,199,254,740,991, which covers nearly everyday uses and is spelled out in the sections below.

When to Use It

How to Use It, Step by Step

1. Decide which form of the number you already have: binary, octal, decimal, or hexadecimal. The tool is two-way, so you can start from any field; you do not need to pick a source and target.
2. Click the matching field, labeled Binary (base 2), Octal (base 8), Decimal (base 10), or Hexadecimal (base 16). The tool starts with the decimal value 42 filled in, so select the existing text and replace it.
3. Type or paste the digits only: 0 and 1 for binary, 0 to 7 for octal, 0 to 9 for decimal, and 0 to 9 plus A to F for hexadecimal. Upper and lower case letters are both accepted in the hex field.
4. Watch the other three fields update with each keystroke. Hexadecimal results are always shown in capital letters, and leading zeros are not shown, so 0010 in binary appears as 10.
5. If a red message appears, the character you just typed does not belong in that base, for example a 2 in the binary field. The field returns to the last valid value; retype using only allowed digits.
6. Clear a field completely and all four become empty, which is a clean way to start over. A field with only spaces is treated as empty too.
7. Press the Copy button beside the field you need. It reads "Copied" for a moment, and the digits are on your clipboard without any 0x or 0b prefix, so add one yourself if your programming language requires it.

Understanding Your Results

The four fields always describe the same quantity. If you enter decimal 1000, the other fields show 1111101000 in binary, 1750 in octal, and 3E8 in hexadecimal. A quick check is length: binary uses roughly 3.3 digits for every decimal digit, octal about 1.1 digits per decimal digit, and hexadecimal about 0.83. Binary should always be the longest string and hexadecimal the shortest, and a result that breaks that ordering means you have typed something unexpected.

Powers of two give a tidy sanity check. 1024 is 10000000000 in binary (a 1 followed by ten zeros), 400 in hex, and 2000 in octal. A value of the form 2^n minus 1 is all ones in binary, and every hex digit is F: 255 is FF and 4095 is FFF. If you are working with fixed widths, such as 8-bit bytes or 16-bit words, count the binary digits and pad with leading zeros yourself, since the tool drops them.

When the number is too large, the tool shows the message "Number is too large to convert precisely." Numbers up to 9,007,199,254,740,991 (binary: fifty-three ones, hexadecimal: 1FFFFFFFFFFFFF) convert exactly. Beyond that, decimal values cannot be represented exactly in a standard JavaScript number, so the tool refuses rather than show a wrong digit. For 64-bit identifiers or cryptographic values, use a tool that supports big integers.

More Worked Examples

Tips for Better Results

• Group binary digits in fours by eye when reading long results. Each group of four maps to exactly one hex digit, so 1111 1010 reads as FA, which makes mental conversion between binary and hex quick.
• Convert hex color pairs one at a time. Splitting FF8800 into FF, 88, and 00 and converting each pair gives the three RGB channel values from 0 to 255.
• For Unix permissions, enter each octal digit separately or all three together and read the binary: the three bits stand for read, write, and execute, and a 1 turns the permission on.
• When your language needs a prefix, add it after copying: 0x for hex, 0b for binary, and a leading 0 or 0o for octal, depending on the language. This tool copies bare digits so you can pick the right form.
• Pad binary results to a fixed width when working with bytes or words. The tool shows 101 rather than 00000101, so add leading zeros up to 8, 16, or 32 digits yourself.
• If you need to convert a fraction or a negative number, convert the whole-number parts separately and handle sign and fractional digits by hand, since this tool supports non-negative integers only.

Common Mistakes to Avoid

• Typing a prefix such as 0x or 0b into a field. The letter x is not a valid hex digit, so it is rejected, and 0b101 in the hex field is read as the plain hex number 0B101, not binary 101.
• Entering a decimal point or minus sign. The fields accept only digits for the chosen base, so fractions and negative numbers are not converted.
• Confusing hex digits with decimal ones, such as reading 10 in hexadecimal as ten. It is sixteen, because the left digit has a place value of 16.
• Forgetting that leading zeros disappear. If a protocol expects a full eight-bit byte, 00001111 and 1111 are the same number but not the same written length.
• Assuming an unlimited range. Beyond about 9 quadrillion, the tool stops, so 64-bit hash values or large database IDs cannot be converted here.

Assumptions and Limits

• The converter handles non-negative whole numbers only, from 0 up to 9,007,199,254,740,991 (2^53 minus 1), the largest integer JavaScript represents without rounding.
• Negative numbers are not converted, so two's complement notation, used by computers for signed values, is outside what this tool shows. A binary string like 11111111 is always read as 255 here, never as minus 1.
• Output uses the standard digit sets with no prefixes, no spaces, and no leading zeros. Hex letters are uppercase.
• For anything involving security keys, financial amounts, or hardware where a single wrong bit matters, double-check the result against the specification or a second tool.

Key Terms

Base (radix)

The number of distinct digits a positional system uses. Binary is base 2, octal base 8, decimal base 10, and hexadecimal base 16.

Bit

A single binary digit, 0 or 1. Eight bits make a byte, which can hold values from 0 to 255.

Hexadecimal

A base-16 system using the digits 0 to 9 and the letters A to F for ten to fifteen. Each hex digit stands for exactly four bits.

Octal

A base-8 system using digits 0 to 7. Each octal digit stands for three bits, which is why Unix permissions are written in it.

Positional notation

A way of writing numbers in which a digit's value depends on its position, equal to the digit times the base raised to the position count.