Convert binary to and from decimal, hexadecimal and octal – including binary fractions – with the calculation steps shown for every conversion. Everything runs locally in your browser.
Binary and Decimal
- Binary to Decimal Converter
Convert a binary number to decimal by summing the place values – each 1 bit contributes its power of two.
- Decimal to Binary Converter
Convert a decimal number to binary using repeated division by two – the steps panel lists every division and remainder for your exact input, however large.
- Binary Fraction to Decimal Converter
Convert a binary number with a fractional part (such as 101.
- Decimal Fraction to Binary Converter
Convert a decimal fraction to binary by repeated multiplication by two.
Binary and Hex
- Binary to Hex Converter
Convert binary to hexadecimal by splitting the bits into 4-bit groups (nibbles) – each group maps to exactly one hex digit.
- Hex to Binary Converter
Convert hexadecimal to binary by expanding every hex digit into its 4-bit pattern.
Binary and Octal
- Binary to Octal Converter
Convert binary to octal by splitting the bits into 3-bit groups – each group is one octal digit 0-7.
- Octal to Binary Converter
Convert octal to binary by expanding every octal digit into its 3-bit pattern.
Binary is the substrate — every other base here is a grouping or an arithmetic transformation of bits. These converters move between binary and its neighbours with the structure visible: place values for decimal, nibbles for hex, triples for octal, negative powers for fractions.
All conversions are exact at any length and computed on your device.
How binary conversion really works
Binary is ordinary positional notation with a base of two: every column is worth twice the column to its right, so the bits of 1101 stand for 8 + 4 + 0 + 1 = 13. Converting binary to decimal is nothing more than adding up the place values of the 1 bits, and converting decimal to binary is the reverse process of repeatedly dividing by two and keeping the remainders. Each converter on this page shows those steps for the exact number you type, which is the fastest way to learn the method well enough to do it on paper.
Between binary and hexadecimal or octal there is an even better shortcut that skips decimal entirely: because 16 is 2⁴ and 8 is 2³, you can convert by regrouping bits — four bits per hex digit, three bits per octal digit — with no arithmetic at all. Fractions work the same way on the other side of the point, where columns are worth 1/2, 1/4, 1/8 and so on. The fraction tools here use exact arithmetic, so a value that repeats forever is reported as repeating instead of being silently rounded.
A few anchors make binary fluency practical: eight bits form a byte whose largest value is 11111111, or 255; 2¹⁰ is 1024, the “kilo” of kibibytes; and every left shift doubles a value while every right shift halves it. Once those landmarks are familiar, most conversions you meet in real work become recognition rather than calculation.
