Binary To Decimal
Free online Binary to Decimal Converter that instantly turns base-2 numbers into decimal.
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The Binary to Decimal Converter instantly turns base-2 numbers into the everyday base-10 values people use. Enter any binary number and get its decimal equivalent in one click — and the explanation below shows exactly how the place-value method works so you can do it yourself.
Two Number Systems, One Value
Binary (base-2) and decimal (base-10) are just different ways of writing the same quantity. Decimal uses ten digits and place values of 1, 10, 100; binary uses two digits and place values that double — 1, 2, 4, 8, 16. Converting between them is about translating those place values, and this tool does the arithmetic instantly.
How to Convert
- Enter the binary number.
- Convert — the tool sums the place values.
- Copy the decimal result.
The Place-Value Method
| Bit | 1 | 0 | 1 | 1 |
|---|---|---|---|---|
| Place value | 8 | 4 | 2 | 1 |
| Contributes | 8 | 0 | 2 | 1 |
Reading 1011: each position has a value that doubles from right to left, and you add the values wherever the digit is 1. Here that's 8 + 0 + 2 + 1 = 11. That's the entire method — assign doubling place values, then sum the 1s.
Why a Byte Holds 256 Values
This method explains a famous number. Eight bits, all set to 1 (11111111), sum to 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. Counting from zero, that's 256 possible values in a single byte — the reason 255 shows up everywhere from color channels to network addresses.
Why Computers Speak Binary
The whole system exists because digital hardware is built from switches that are either on or off. Those two states map perfectly onto 1 and 0, making binary the simplest and most reliable way to store and process information electronically. Converting to decimal is how we translate the machine's language back into ours.
Accurate, Free, and Private
The converter sums place values at full precision in your browser, with nothing stored. Convert binary of any length, free.
Frequently Asked Questions
How do I convert binary to decimal?
Give each binary digit a place value that doubles from right to left (1, 2, 4, 8, 16...), then add the values where the digit is 1. For example, 1011 is 8 + 0 + 2 + 1 = 11. The tool sums these instantly.
What is the place value in binary?
Binary is base-2, so each position is worth twice the one to its right: the rightmost is 1, then 2, 4, 8, 16, and so on. A digit contributes its place value only when it's a 1.
Why is binary called base-2?
Because it uses only two digits, 0 and 1. Decimal is base-10 with ten digits (0–9). The 'base' is simply how many distinct digits a number system uses, which determines how place values grow.
What's the largest value in 8 bits?
Eight binary digits represent 0 to 255 — that's 11111111, which sums to 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This is why a single byte holds 256 possible values.
Why do computers use binary?
Digital hardware is built from switches that are either on or off, which map naturally to 1 and 0. Binary is the simplest, most reliable way to represent and process information electronically.
Can it handle long binary numbers?
Yes. The converter sums the place values for binary of any length precisely, so large numbers convert without rounding errors.
Is my data private?
Yes. Conversion happens in your browser and nothing is uploaded or stored.
Is this tool free?
Yes — free, instant, and unlimited, with no signup.