Binary / Hex Converter

How this is calculated

Your value is first converted to decimal, regardless of which base you entered it in. From decimal, it's re-expressed in binary, hexadecimal, and octal using repeated division and remainders.

Number bases explained

A number base (or radix) defines how many unique digits are available before carrying to the next place value. Decimal (base 10) uses 0-9; binary (base 2) uses only 0-1; hexadecimal (base 16) uses 0-9 and A-F; octal (base 8) uses 0-7.

Quick reference table

Decimal	Binary	Hex	Octal
10	1010	A	12
100	1100100	64	144
255	11111111	FF	377

Common pitfalls

• Forgetting leading context — the same digits mean different values in different bases; "10" is ten in decimal but two in binary.
• Mixing hex letters and numbers — hex digits A-F stand for 10-15, not literal letters, so "1A" in hex equals 26 in decimal.
• Padding assumptions — binary and hex results here aren't zero-padded to a fixed width (like 8 or 16 bits); add leading zeros yourself if your context requires a fixed length.

Tips

• Every hex digit corresponds to exactly 4 binary bits, making hex a compact shorthand for binary data.
• Color codes in web design (like #1F2A44) are hexadecimal — the same conversion applies.

Frequently asked questions

How do you convert decimal to binary? Repeatedly divide the number by 2 and record the remainders; reading the remainders from last to first gives the binary form. For example, 13 in binary is 1101.

How do you convert binary to hexadecimal? Group the binary digits into sets of four starting from the right, then convert each group to its hex digit. Converting through decimal first also works and is easier by hand.

What is hexadecimal used for? Hexadecimal is widely used in programming and computing to represent memory addresses, color codes (like #FF5733), and binary data compactly, since each hex digit represents exactly 4 binary bits.

What is the largest value one byte (8 bits) can hold? An 8-bit byte can represent decimal values from 0 to 255 (binary 00000000 to 11111111, or hex 00 to FF).

Why does hexadecimal use letters A-F? Hexadecimal is base 16, so it needs 16 distinct digits. After 0-9, the letters A through F represent the values 10 through 15.

Worked examples

Example 1 — Decimal to others: 255 → binary 11111111, hex FF, octal 377.

Example 2 — Binary input: 1101 (binary) → decimal 13, hex D, octal 15.

Example 3 — Hex input: 1A (hex) → decimal 26, binary 11010, octal 32.

Practical examples of binary, hex and octal

One value in four bases

Decimal	Binary	Hex	Octal
10	1010	A	12
47	101111	2F	57
255	11111111	FF	377

Converting hex by hand: 2F = 2 × 16 + 15 = 47.

Where each base is used

• Binary shows the bits that hardware and low-level code work with.
• Hexadecimal is a compact way to write bytes, memory addresses and colours. For example, #FF8800 means red 255, green 136 and blue 0.
• Octal appears in Unix file permissions, where 755 means read, write and execute for the owner and read and execute for everyone else.

Writing prefixes correctly

Programming languages often mark the base with a prefix: 0b for binary, 0x for hexadecimal and sometimes 0o or a leading zero for octal. Enter just the digits in the converter, and add the prefix yourself when you paste the result into code.

More questions

Why group binary digits in fours? Four bits map exactly to one hex digit, which makes conversion between binary and hex quick to do by eye.

Does hexadecimal care about upper or lower case letters? No. A-F and a-f represent the same values; the case is only a style choice.