Convert Binary to Decimal

Feb 11, 2022

A binary number is a number expressed in base-2, as opposed to conventional decimal numbers in base-10.

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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) // 42

The toString() method also handles non-integers and negative numbers. For example:

x = -101010
parseInt(x, 2); // -42

x = 101010.101010;
parseInt(x, 2); // 42

No 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:

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:

  1. 101010
  2. 101010 => 0 + 1 == 1
  3. 1 * 2 + 0 == 2
  4. 2 * 2 + 1 == 5
  5. 5 * 2 + 0 == 10
  6. 10 * 2 + 1 == 21
  7. 21 * 2 + 0 == 42

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