How To Convert Binary Fraction To Decimal

Javascript has the function parseInt() which can help convert integer in a binary form into its decimal equivalent: parseInt('101', 2) // 5 However, I need to convert binary fract

Solution 1:

This question asks whether there is some JavaScript standard for parsing binary floating-point numbers, as if parseFloat() could have taken a second radix parameter to parse the binary number 0.101 like this: parseFloat('0.101', 2).

While there is no such standard, there is an easy and direct way to solve this.

If we represent the binary number 0.101 as a binary fraction, it is easily converted to a decimal fraction:

0.101₂ = 101₂/1000₂ = (5/8)₁₀ = 0.625

The following one-line expression translates this to JavaScript. Here, num could be any type of binary number (represented as a string), including negative numbers:

parseInt(num.replace('.', ''), 2) / Math.pow(2, (num.split('.')[1] || '').length)

The solution is easily adapted to floating-point numbers in any base between 2 and 36, and we can wrap it in our own parseFloatRadix() function:

function parseFloatRadix(num, radix) {
  return parseInt(num.replace('.', ''), radix) /
    Math.pow(radix, (num.split('.')[1] || '').length)
}

test('0.101',  2, 0.625);
test('0.011',  2, 0.375);
test('0.0011', 2, 0.1875);
test('-011',   2, -3);
test('011',    2,  3);
test('-1100.0011', 2, -12.1875);
test('1100.0011',  2,  12.1875);
test('0.00011001100110011001100', 2, 0.09999990463256836);

test('ABC',     16, 2748);
test('-0.DEF',  16, -0.870849609375);
test('ABC.DEF', 16, 2748.870849609375);

test('-102.201', 3, -11.703703703703704);
test('-Z.ZZZ',  36, -35.99997856652949);

function test(num, radix, expected){
  let result = parseFloatRadix(num, radix);
  console.log(num + ' (base ' + radix +') --> ' + result + 
    (result === expected ? ' (OK)' : ' (Expected ' + expected + ')'));
}

Solution 2:

You can split the number (as string) at the dot and treat the integer part with an own function and the fraction part with another function for the right value.

The solution works with other bases as well.

function convert(value, base = 2) {
    var [integer, fraction = ''] = value.toString().split('.');

    return parseInt(integer, base) + (integer[0] !== '-' || -1) * fraction
        .split('')
        .reduceRight((r, a) => (r + parseInt(a, base)) / base, 0);
}

console.log(convert(1100));           //    12
console.log(convert(0.0011));         //     0.1875
console.log(convert(1100.0011));      //    12.1875

console.log(convert('ABC', 16));      //  2748
console.log(convert('0.DEF', 16));    //     0.870849609375
console.log(convert('ABC.DEF', 16));  //  2748.870849609375

console.log(convert('-ABC.DEF', 16)); // -2748.870849609375
console.log(convert(-1100.0011));     //   -12.1875

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Solution 3:

TL;DR:

const convert = (s, b) => (+((s = s.toString().trim().split("."))[0][0] !== "-") || -1) * ((parseInt(s[0].replace("-", ""), (b = +b || 2))) + (s[1].split("").reduceRight((n, d) => (n + parseInt(d, b)) / b, 0)));

---

Nina Scholz has a nice example, but it doesn't work with negative numbers (plus other issues).
So, this is an improved one:

/**
 * @param {string} input
 * @param {number} [base]
 * @returns {number}
 */
function convert(input, base = 2) {
    const [ integerRaw, decimalRaw = "" ] = input.toString().trim().split(".");

    const integer = parseInt(integerRaw.replace("-", ""), base);
    const decimal = decimalRaw.split("").reduceRight((sum, num) => (sum + parseInt(num, base)) / base, 0);

    return (integerRaw.startsWith("-") ? -1 : 1) * (integer + decimal);
}

convert("1100.0011"); // 12.1875
convert("-1100.0011"); // -12.1875
convert("-Z.ZZZ", 36); // -35.99997856652949

As I know, JavaScript doesn't provide such built-in functionality.

Solution 4:

But I'm wondering whether there is anything standard already.

No according my knowledge

I think you need to create your own function:

  function toDecimal(string, radix) {
    radix = radix || 2;
    var s = string.split('.');
    var decimal = parseInt(s[0], radix);

    if(s.length > 1){
       var fract = s[1].split('');

       for(var i = 0, div = radix; i < fract.length; i++, div = div * radix) {
          decimal = decimal + fract[i] / div;
       }
    }
    return decimal;
  }

Solution 5:

You can create javascript extension method like parseInt as I have created method parseBinary which works just link parseInt.

String.prototype.parseBinary = function parseBinary() {
  var radix = 2;
  var s = this.split('.');
  var decimal = parseInt(s[0], radix);

  if(s.length > 1){
    var fract = s[1].split('');

    for(var i = 0, div = radix; i < fract.length; i++, div = div * radix)
    {
      decimal = decimal + fract[i] / div;
    }
  }
  return decimal;
};

To use this method you can call it using following code.

var str = "0.101";
alert(str.parseBinary());

Here is a working example of javascript code

String.prototype.parseBinary = function parseBinary() {
  var radix = 2;
  var s = this.split('.');
  var decimal = parseInt(s[0], radix);

  if(s.length > 1){
    var fract = s[1].split('');

    for(var i = 0, div = radix; i < fract.length; i++, div = div * radix)
    {
      decimal = decimal + fract[i] / div;
    }
  }
  return decimal;
};

var str = "0.101";
alert(str.parseBinary());