Binary to Decimal Converter
Binary, decimal, hexadecimal and octal — type in any field and the other three convert live, exact even for very large numbers.
How number bases work
All four fields show the same number — only the base differs. Decimal uses powers of ten, binary powers of two, hex powers of sixteen. Because 16 is 2⁴, each hex digit maps to exactly four binary digits, which is why hex is the standard shorthand for binary.
Type in any field
Enter a decimal number, a binary string, hex (with or without 0x) or octal.
Read the other bases
All fields stay in sync live; invalid digits for a base are flagged immediately.
Check the bit length
Below the fields you see how many bits the number needs — useful for sizing data types.
Reading binary without counting on fingers
The fastest mental route between binary and anything else goes through hex: split the binary string into groups of four from the right, and translate each group to one hex digit — 1111 1111 is ff, which is 255. A few anchors worth memorizing: 1010 is a (10), 1111 is f (15), and a byte tops out at ff = 255. The converter uses arbitrary-precision math, so unlike many calculators it stays exact past 32 and 64 bits — handy for hashes, IDs and bit masks.
Frequently asked questions
How do I convert binary to decimal by hand?
Each binary digit is a power of two, read from the right: 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 11. The converter does this instantly for numbers of any length.
Why do programmers use hexadecimal?
One hex digit represents exactly four binary digits, so hex is a compact, lossless way to write binary: 11111111 becomes ff. That's why memory addresses, color codes and byte dumps use hex.
How large can the numbers be?
Effectively unlimited — the converter uses arbitrary-precision integers, so it stays exact far beyond the 32-bit and 64-bit limits where ordinary calculators start rounding.
Does the converter handle negative numbers or fractions?
It converts non-negative whole numbers, which covers the standard use cases. Negative values in computing depend on a chosen bit width (two's complement), so they aren't a single convertible value without that context.