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

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.