Binary, decimal and hexadecimal

The same 42, three representations

Decimal 42 is written as 101010 in binary and 2A in hexadecimal. Binary weights 32, 8 and 2 are on. Adding them gives 42.

To convert binary to hexadecimal, group bits into blocks of four from the right. Leading zeros preserve the value: 0010 1010 becomes 2 A. Hexadecimal A means ten, so 2A = 2 × 16 + 10 = 42.

Each position has a weight

Positions start at zero on the right. The tool shows each nonzero digit’s contribution and a table of successive divisions: divide the decimal value by the target base, keep the remainder and repeat with the quotient. Read the remainders in reverse order.

Bit buttons show their position and weight; their accessible names include the full decimal weight. Changing the input base preserves the number, and toggling bits updates every representation.

64-bit unsigned integers, without rounding

The range is 0 to 18,446,744,073,709,551,615 inclusive: 2⁶⁴ − 1. BigInt provides exact integer arithmetic, avoiding the precision loss of ordinary JavaScript numbers beyond 2⁵³ − 1.

Negative numbers, fractions, scientific notation, separators and prefixes such as 0x or 0b are not accepted. Visible width does not alter or truncate the number; it expands to the next available size if needed. This is not two’s complement or floating-point representation.

Common mistakes

• Assuming 10 means the same number in every base: it means two in binary and sixteen in hexadecimal.
• Counting the first bit as position 1: the rightmost bit is 2⁰.
• Interpreting F as fifteen positions: it is one digit with the value 15.
• Converting 64-bit integers with a numeric type that rounds large values.

Try it yourself