How do you convert numbers between different bases in JavaScript?

The API

To convert to a number from a hex string:

parseInt(string, radix)

• string: Required. The string to be parsed

• radix: Optional. A number (from 2 to 36) that represents the numeral system to be used

To convert from a number to a hex string:

NumberObject.toString(radix)

• radix: Optional. Specifies the base radix you would like the number displayed as.

Example radix values:

• 2 - The number will show as a binary value
• 8 - The number will show as an octal value
• 16 - The number will show as an hexadecimal value

Example Usage

Integer value to hex:

var i = 10;
console.log( i.toString(16) );

Hex string to integer value:

var h = "a";
console.log( parseInt(h, 16) );

Integer value to decimal:

 var d = 16;
 console.log( d.toString(10) );

You may try the following code, which also supports arbitrary precision numbers (larger than 2^53).

function convertBase(str, fromBase, toBase) {

    const DIGITS = "0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ+/";

    const add = (x, y, base) => {
        let z = [];
        const n = Math.max(x.length, y.length);
        let carry = 0;
        let i = 0;
        while (i < n || carry) {
            const xi = i < x.length ? x[i] : 0;
            const yi = i < y.length ? y[i] : 0;
            const zi = carry + xi + yi;
            z.push(zi % base);
            carry = Math.floor(zi / base);
            i++;
        }
        return z;
    }

    const multiplyByNumber = (num, x, base) => {
        if (num < 0) return null;
        if (num == 0) return [];

        let result = [];
        let power = x;
        while (true) {
            num & 1 && (result = add(result, power, base));
            num = num >> 1;
            if (num === 0) break;
            power = add(power, power, base);
        }

        return result;
    }

    const parseToDigitsArray = (str, base) => {
        const digits = str.split('');
        let arr = [];
        for (let i = digits.length - 1; i >= 0; i--) {
            const n = DIGITS.indexOf(digits[i])
            if (n == -1) return null;
            arr.push(n);
        }
        return arr;
    }

    const digits = parseToDigitsArray(str, fromBase);
    if (digits === null) return null;

    let outArray = [];
    let power = [1];
    for (let i = 0; i < digits.length; i++) {
        digits[i] && (outArray = add(outArray, multiplyByNumber(digits[i], power, toBase), toBase));
        power = multiplyByNumber(fromBase, power, toBase);
    }

    let out = '';
    for (let i = outArray.length - 1; i >= 0; i--)
        out += DIGITS[outArray[i]];

    return out;
}

Usage:

console.log(convertBase("5a2a9c826c75045be9ba8fbffc80c6f25a2a9c826c75045be9ba8fbffc80c6f2",16,64));
// Returns: 5EGD89ItghrWrGfL/O0NL9qaFO2r7k4m+CWzX/YwcrO

console.log(convertBase("5EGD89ItghrWrGfL/O0NL9qaFO2r7k4m+CWzX/YwcrO",64,16));
// Returns: 5a2a9c826c75045be9ba8fbffc80c6f25a2a9c826c75045be9ba8fbffc80c6f2

The basic code has been found here, I have a bit improved it to also support up to base 64.

I came to this post needing to convert from base 10 to 62 and vice-versa. Whilst the solutions here are great, parseInt and toString only support base 2 to 36. So if anyone finds themselves in a similar position to me needing base 2 to 62, I've pasted my solution below.

https://gist.github.com/ryansmith94/91d7fd30710264affeb9

function convertBase(value, from_base, to_base) {
  var range = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ+/'.split('');
  var from_range = range.slice(0, from_base);
  var to_range = range.slice(0, to_base);
  
  var dec_value = value.split('').reverse().reduce(function (carry, digit, index) {
    if (from_range.indexOf(digit) === -1) throw new Error('Invalid digit `'+digit+'` for base '+from_base+'.');
    return carry += from_range.indexOf(digit) * (Math.pow(from_base, index));
  }, 0);
  
  var new_value = '';
  while (dec_value > 0) {
    new_value = to_range[dec_value % to_base] + new_value;
    dec_value = (dec_value - (dec_value % to_base)) / to_base;
  }
  return new_value || '0';
}