Binary Converter

What is binary?

Binary is base 2: it writes every number using only 0 and 1. Each position is worth twice the one to its right, so where decimal counts in ones, tens, and hundreds, binary counts in ones, twos, fours, and eights. Computers use it because a circuit only has to tell two states apart, off and on, rather than ten.

How to use this converter

1. 1

   Type your value

   Enter the number or text you want to convert in the Input Value field.

2. 2

   Pick the base you are starting from

   Set Input Base to match what you typed: Decimal, Binary, Octal, Hexadecimal, or Text.

3. 3

   Read every other representation

   The results update as you type and show all the remaining bases at once, so you do not choose a target base.

4. 4

   Copy what you need

   Copy the line you want straight from the results.

There is no target base to choose. Whatever you put in, the converter shows all the other representations at the same time.

Binary to decimal: 10110101

Give each bit its place value, then add the ones sitting above a 1.

Adding the highlighted values: 128 + 32 + 16 + 4 + 1 = 181. So binary 10110101 is 181 in decimal.

Binary to hexadecimal: 10110101 to B5

Hex is quicker than going through decimal, because one hex digit is exactly four bits. Split the byte into two groups of four and convert each on its own: 1011 is 8 + 2 + 1, which is 11, written B. Then 0101 is 4 + 1, which is 5. Put them back together and 10110101 is B5. Checking against the decimal above, B5 is 11 times 16 plus 5, which is 181.

Binary to text: reading bytes as ASCII

Text mode reads eight bits at a time and looks each byte up as a character. Take 01001000 01101001. The first byte is 64 + 8, which is 72, and 72 is the letter H. The second is 64 + 32 + 8 + 1, which is 105, the letter i. Together they spell Hi. Set Input Base to Binary and paste both bytes to see the same result.

Negative numbers: two’s complement

This converter takes non-negative values only, so negatives are worth understanding by hand. Computers store them in two’s complement: write the positive value, flip every bit, then add 1. For -5 in eight bits, +5 is 00000101, flipping every bit gives 11111010, and adding 1 gives 11111011.

Those same eight bits are 251 when read as an unsigned number, which is what this tool will show you if you enter them. Whether the byte means -5 or 251 depends entirely on which convention the program reading it uses, and nothing in the bits themselves records the choice.

Quick reference

Frequently asked questions

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