Convert Binary to Decimal
A binary number is a number expressed in base-2, as opposed to conventional decimal numbers in base-10.
Below is a live calculator.
| Binary | Decimal | |
|---|---|---|
| ➜ |
We also have a tool to convert decimal to binary.
How the Calculator Works
Converting binary numbers to decimal is easy.
For example, let x = '101010' creates a new variable x that contains the number as a string 101010.
JavaScript has a parseInt() method that takes a binary and radix parameter, and returns a number.
Calling parseInt(binary, radix) tells JavaScript to convert binary to a number containing the decimal representation of 101010.
If binary is not a string, it will be converted to one using the toString() function.
let x = '101010';
parseInt(x, 2) // 42The toString() method also handles non-integers and negative numbers. For example:
x = -101010
parseInt(x, 2); // -42
x = 101010.101010;
parseInt(x, 2); // 42No Technology Method
How do you quickly convert 101010 to 42 without a computer?
It takes some practice to make it easy, but here's a few ways to convert a binary string to a decimal number.
One method discussed is doubling, described below:
- Take the binary string.
- Starting from the left, double your previous total and add the current digit.
- Double your current total and add the next leftmost digit.
- Repeat the previous step until you have gone through the entire string.
Below is a JavaScript function that implements the above procedure:
function toDecimal(v) {
let binary = '';
if(typeof v == 'string') {
binary = v.split();
} else {
binary = v.toString().split();
}
let decimal = 0;
for(let i = 0; i < binary.length; i++) {
decimal = (decimal * 2) + binary[i];
}
return decimal;
}Here's what the procedure looks like with 101010:
- 101010
- 101010 => 0 + 1 == 1
- 1 * 2 + 0 == 2
- 2 * 2 + 1 == 5
- 5 * 2 + 0 == 10
- 10 * 2 + 1 == 21
- 21 * 2 + 0 == 42