JavaScript functions for converting between numerical bases two through sixteen.

baseConvert.js

/*********************************************************
 * Converts to and from any base in the set (2,16).
 * Assumes that the digitString and inputBase match.
 * @param {String} digitString is a sequence of digits.
 * @param {Number} inputBase is in the set (2,16)
 * @param {Number} outputBase is in the set (2,16)
 * @return {String} result is a string of digits 2-F
 ********************************************************/
function baseConvert( digitString, inputBase, outputBase ) {
  
  // First, convert the inputNumber to its decimal form.
  var decimalValue = 0;
  if (inputBase == 10) decimalValue = parseInt(digitString, 10);
  else decimalValue = convertToDecimal(digitString, inputBase);

  // Next, convert the decimalValue to its outputBase form.
  if (outputBase == 10) return decimalValue;
  return convertToBase(decimalValue, outputBase);
}

/*********************************************************
 * Converts from any base in the set (2,16) to decimal.
 * Assumes that the inputNumber and inputBase match.
 * @param {String} inputDigits is a string of digits
 * @param {Number} inputBase is in the set (2,16)
 * @return {Number} a decimal value 
 ********************************************************/
function convertToDecimal( inputDigits, inputBase ) {

  // decimalResult is a sum of products in base-ten.
  var decimalResult = 0;

  // placeValue represents the value of a digit position.
  // The rightmost position is the one's place (any_base ^ 0).
  var placeValue = 1;

  /* STEP 1: Extract the rightmost digit from the string.
   * STEP 2: Multiply the digit by its position value.
   * STEP 3: Add that product to the decimalResult.
   * STEP 4: Remove the rightmost digit from the string.
   * STEP 4: Repeat for all digits.
   */
  while ( inputDigits.length > 0 ) {

    // Extract the rightmost character from inputDigits.
    var digitChar = inputDigits[ inputDigits.length-1 ];

    // Convert this character to its value in base-ten.
    var digitNum = parseInt( ("" + digitChar), inputBase );

    // Find the value of the digit based on its position.
    var digitValue = digitNum * placeValue;

    // Add this product to the result sum.
    decimalResult += digitValue;

    // Increment the base place exponentially.
    placeValue *= inputBase;

    // Shorten the digit string by removing the rightmost char.
    inputDigits = inputDigits.slice(0, (inputDigits.length-1) );
  }

  // Return the sum of digit values in base-ten.
  return decimalResult;
}

/*********************************************************
 * Converts from decimal to any base in the set (2,16).
 * @param {Number} decimalInput is a base-ten number 
 * @param {Number} outputBase is in the set (2,16)
 * @return {String} digitString in the outputBase
 ********************************************************/
function convertToBase( decimalInput, outputBase ) {

  // letterDigits represent digits 10 through 16.
  var letterDigits = ['A','B','C','D','E','F'];

  // digitString is a number in the outputBase to return.
  var digitString = "";
   
  // placeValue is a power of ten 
  var placeValue = 1;
  
  /* STEP 1: Divide the decimalInput by the outputBase.
   * STEP 2: Store the remainder of the division as digit.
   * STEP 3: Append this digit to the front of digitString.
   * STEP 4: Repeat for all digits.
   */
  while ( decimalInput > 0 ) {
    
    // Extract the rightmost digit from decimalInput.
    var digit = decimalInput % outputBase;

    // If the digit is higher than 9,
    // convert it to the appropriate character.
    if (digit > 9) {
      for (var i = 10; i <= 16; i++) {
        if (digit == i) {
          // Append the letter digit to digitString.
          digitString = letterDigits[i-10] + digitString;
          break;
        }
      }
    }
    // Otherwise, append the digit to digitString as is.
    else digitString = digit + digitString;

    // Remove te rightmost digit from decimalInput.
    decimalInput = Math.floor(decimalInput / outputBase);
  }
 
   // Return the sum of digit values.
   return digitString;
}