Number Base Converter — Binary, Octal, Decimal & Hex

Number Base Converter: Binary, Octal, Decimal and Hexadecimal in One Place

Computers store everything in binary, people count in decimal, and programmers spend much of their day in hexadecimal. Moving between these number systems is routine for students of computer science and electronics, for developers reading memory addresses, colour codes and bit masks, and for anyone preparing for exams with number-system questions. This free number base converter does the conversion instantly and exactly. Type a number, tell it which base it is in, and it shows the same value in binary, octal, decimal, hexadecimal, base 32 and base 36 all at once.

Unlike calculators that quietly lose precision once numbers get big, this tool uses exact big-integer arithmetic. A 64-bit value, a 128-bit hash or a 300-digit number converts without a single wrong digit. It also understands the prefixes programmers type — 0x, 0b, 0o — ignores spaces and underscores, and tells you exactly which character is invalid if you make a typo. Everything runs in your browser.

How to Use the Converter

1. Type your number in the Number box. You can write 255, 0xFF, 0b1111_1111 or 1111 1111.
2. Choose the base it is written in — Decimal, Binary, Octal, Hexadecimal, or Other base… for anything from 2 to 36.
3. Read the results. The table shows binary, octal, decimal, hexadecimal, base 32 and base 36. The line above it confirms how the input was read and how many bits the number needs.
4. Adjust the display. Turn digit grouping on or off (binary in fours, octal in threes, hex in pairs, decimal with commas), and choose uppercase or lowercase letters.
5. Copy All puts every conversion on your clipboard, one per line.

How Number Bases Work

A number base, or radix, is how many different digits a positional system uses. In base 10 we have ten digits, 0 to 9, and each position is worth ten times the one to its right: units, tens, hundreds. In base 2 there are only two digits, 0 and 1, and each position is worth twice the previous one: 1, 2, 4, 8, 16 and so on. Hexadecimal uses sixteen digits — 0 to 9 and then A to F for ten to fifteen — so positions are worth 1, 16, 256, 4,096.

The value of any number is the sum of each digit times its place value:

value = dₙ × bⁿ + … + d₂ × b² + d₁ × b + d₀

The converter reads your input this way into an exact integer, then writes that integer out in each target base by repeated division.

Worked Examples

Decimal to binary: 13

Divide by 2 and note the remainders: 13 ÷ 2 = 6 remainder 1; 6 ÷ 2 = 3 r 0; 3 ÷ 2 = 1 r 1; 1 ÷ 2 = 0 r 1. Reading the remainders from bottom to top gives 1101.

Binary to decimal: 1101

1 × 8 + 1 × 4 + 0 × 2 + 1 × 1 = 13.

Hex to decimal: 7EA

7 × 256 + 14 × 16 + 10 × 1 = 1,792 + 224 + 10 = 2,026. In binary that is 111 1110 1010 and in octal 3752.

Decimal to hex: 255

255 ÷ 16 = 15 remainder 15. Fifteen is F, so 255 = FF. In binary it is 1111 1111 — eight ones, the largest value a byte can hold.

A big number: 2⁶⁴ − 1

18,446,744,073,709,551,615 is the largest unsigned 64-bit integer. In hex it is FFFF FFFF FFFF FFFF and in binary sixty-four ones. Ordinary JavaScript numbers can't hold it exactly — they are precise only up to 2⁵³ − 1 = 9,007,199,254,740,991 — but this converter shows every digit correctly.

Quick Reference Table

Shortcuts Between Binary, Octal and Hex

Because 8 = 2³ and 16 = 2⁴, you can convert between binary, octal and hex without going through decimal at all. For hex, split the binary number into groups of four from the right and replace each group with one hex digit: for 2,026 the binary is 111 1110 1010; pad the leftmost group to 0111, and 0111 1110 1010 becomes 7 E A, or 7EA. For octal, use groups of three: 011 111 101 010 → 3752. The grouping option in the converter displays binary in exactly these blocks, which makes it easy to check work by hand.

Where You Meet Different Bases

• Colour codes. A web colour like #FF8800 is three hex bytes — red 255, green 136, blue 0. Our hex to RGB converter does this conversion directly.
• File permissions. chmod 755 is octal: 7 = rwx for the owner, 5 = r-x for group and others.
• Memory addresses and bit masks. Debuggers, register maps and network masks are written in hex because each digit is exactly four bits.
• Hashes and IDs. SHA-256 hashes from our hash generator and UUIDs are long hex strings; base 36 is popular for short, readable IDs.
• Exams. Number-system conversion is a standard topic in school computer science, digital electronics and aptitude tests.

Why Computers Use Binary

Digital circuits are built from switches that are either on or off, so two states are the most reliable thing to store and detect. A single binary digit is a bit; eight bits make a byte, which can represent 2⁸ = 256 different values, from 0 to 255. Larger quantities use more bytes: 16 bits hold 65,536 values, 32 bits about 4.29 billion, and 64 bits about 18.4 quintillion. The converter's bit count tells you how many bits a number needs — useful when you are choosing a data type or checking whether a value will overflow a field.

Long strings of ones and zeros are hard for people to read, which is why hexadecimal became the standard shorthand. Each hex digit stands for exactly four bits, so a byte is always two hex digits and a 32-bit value is always eight. Octal was popular on older machines whose word sizes were multiples of three bits, and it survives today mainly in Unix permissions.

A Short Note on Two's Complement

When you see a negative number in a debugger, it is usually in two's complement form. To get it for an 8-bit value, write the positive number in binary, flip every bit and add one: 5 is 0000 0101, flipped is 1111 1010, plus one is 1111 1011, which is FB in hex — that is how −5 looks in a byte. The same −5 in 16 bits is FFFB. Because the pattern depends on the width, this converter shows −5 as −101 in binary, the width-independent value. If you need the bit pattern, convert 2ⁿ minus the absolute value: for 8 bits, 256 − 5 = 251, which is FB.

Tips for Practising Conversions

• Memorise the powers of two up to 2¹⁰ = 1,024; they make binary-to-decimal conversion much faster.
• Learn the sixteen four-bit patterns for 0–F; hex and binary then convert by sight.
• Check your hand-worked answers with the converter, and read the grouped binary to spot where an error crept in.

Prefixes, Validation and Edge Cases

If the input starts with 0x, 0b or 0o, the converter reads it in that base and tells you it did so. There is one careful exception: in bases where the prefix letter is itself a valid digit, the text is taken literally. In hexadecimal, for example, b is a digit, so 0b12 typed as hex means the hex number B12 rather than a binary prefix. Spaces and underscores — common digit separators in code — are stripped before conversion. If a character is not a valid digit for the base, such as 2 in binary or G in hex, you get a clear message naming it.

Negative numbers are shown with a minus sign. Hardware stores negative integers in two's complement, but that representation depends on a fixed width (8, 16, 32 or 64 bits), so this tool shows the mathematical value instead. Fractions are not supported; the converter works with whole numbers.

One more clarification: the "Base 32" row is radix 32, using digits 0–9 and a–v. It is not the same as RFC 4648 Base32 encoding, which turns bytes into text using A–Z and 2–7. For encoding text or files, use our Base64 encoder and decoder instead.

Number Base Converter — Key Facts

Frequently Asked Questions

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