getNumberInBase.js

#!/usr/bin/env node

var logging = false;

var raiseTo = function(number, power) {
    var value = number;
    for (var i = 1; i < power; i++) {
        value = value*number;
    }
    return value;
};

var getNumberInBase = function(number, digits) {
    var base = digits.length; // What is the biggest number a digit can represent in each place?

    // Figure out how many digits we'll need
    var numberDigits = [0]; // Initialize a list to hold our answer
    // Add digits to our list until the base raised to the number of digits is bigger than our number
    while (raiseTo(base, numberDigits.length) <= number) { numberDigits.push(0); }

    // Now we have a list of the right number of 0's.
    // We're going to go through and subtract from our number to distribute amongst the digits, starting with the biggest
    var remaining = number;
    numberDigits.forEach(function(digit, index) { // For each place value, starting with the biggest
        var placeValue = raiseTo(base,numberDigits.length-index-1); // Compute our place value (base ^ current index), -1 because length is one bigger than our place value
        logging ? console.log("Looking at the the", placeValue+"'s", "place…") : null;
        
        // Iterate from the beginning to the end of our digits, testing which one is bigger than our remainder
        var testDigit = 0;
        while (testDigit*placeValue <= remaining) { testDigit++; }
        // At this point, testDigit*placeValue is bigger than the remainder, so we know which digit this placeValue needs
        // Note that we subtract one from testDigit because our while loop stops once it's too big, so we want to back up one

        logging ? console.log("Setting to", digits[testDigit-1]) : null;
        numberDigits[index] = digits[testDigit-1];

        // Subtract the value we've just calculated from our remainder
        remaining -= placeValue*(testDigit-1);
        logging ? console.log("Now", remaining, "remains…") : null;
    });
    
    return numberDigits.join('');
};

var tests = [
{
    number: 80,
    digits: [0,1,2,3,4,5,6,7,8,9]
},
{
    number: 80,
    digits: [0,1]
},
{
    number: 80,
    digits: ["A", "B", "C", "D"]
},
{
    number: 80,
    digits: ["😋", 2, "💩", "🎨", 5, "🐶", "🐿"]
}
];

tests.forEach(function(test){
    console.log(
        "Converting", test.number, 
        "from base 10 to", test.digits, 
        "yields", getNumberInBase(test.number, test.digits)
        );
});