VCHS Computer Science: Positional Number System

Digit Separator:

Positional Number System 1

Base:

Radix:

Digits:

Numeral:

Position Number System 2

Base:

Radix:

Digits:

Numeral:

Source Code

Digit Separator:
<select id="digit-separator">
  <option value="">None ('')</option>
  <option value=",">Comma (',')</option>
  <option value=" " selected="">Space (' ')</option>
</select>
<p></p><h3>Positional Number System 1</h3><p></p>
<p>Base: <span id="base-pns-1" value="tbd"></span>
</p><p>Radix: <span id="radix-pns-1" value="tbd"></span>
</p><p>Digits: <input id="digits-pns-1" style="width:24em" value="O I II III IIII V VI VII VIII VIIII"></p>
<p>Numeral: <input id="numeral-pns-1" style="width:32em" value="IIII II"></p>
<p></p><h3>Position Number System 2</h3><p></p>
<p>Base: <span id="base-pns-2" value="tbd"></span>
</p><p>Radix: <span id="radix-pns-2" value="tbd"></span>
</p><p>Digits: <input id="digits-pns-2" style="width:24em" value="0 1"></p>
<p>Numeral: <span id="numeral-pns-2"></span></p>
<p>
  <button id="convert-button">Convert</button>
  <span id="error-message" style="color: red"></span>
</p>

<script>
const digitSeparatorElement = document.getElementById("digit-separator");
const digitsPNS1Element = document.getElementById("digits-pns-1");
const digitsPNS2Element = document.getElementById("digits-pns-2");
const basePNS1Element = document.getElementById("base-pns-1");
const basePNS2Element = document.getElementById("base-pns-2");
const radixPNS1Element = document.getElementById("radix-pns-1");
const radixPNS2Element = document.getElementById("radix-pns-2");
const numeralPNS1Element = document.getElementById("numeral-pns-1");
const numeralPNS2Element = document.getElementById("numeral-pns-2");
const convertButton = document.getElementById("convert-button");
const errorMessageElement = document.getElementById("error-message");

digitsPNS1Element.addEventListener("keydown", clearAnswer);
digitsPNS2Element.addEventListener("keydown", clearAnswer);
numeralPNS1Element.addEventListener("keydown", clearAnswer);
convertButton.addEventListener("click", tryConvertNumber);

function clearAnswer() {
  numeralPNS2Element.innerHTML = "";
  basePNS1Element.innerHTML = "tbd";
  basePNS2Element.innerHTML = "tbd";
}

function PositionalNumberSystem(config) {

"use strict";

/* Private Values */

const SEPARATOR = getSeparator(config);
  const DIGITS = getDigits(config);
  const VALUES = getValues(DIGITS);
  const BASE = getBase(DIGITS);
  const RADIX = BASE;
  const DIGIT_ZERO = getZeroDigit(DIGITS);
  const DIGIT_ONE = getOneDigit(DIGITS);
  const NUMBER_ZERO = digitToNumber(DIGIT_ZERO);
  const NUMBER_ONE = digitToNumber(DIGIT_ONE);
  const incrementByOne = incrementByOne_Recursively;
  //const incrementByOne = incrementByOne_ByAddingTwoNumbers;
  const addTwoNumbers = addTwoNumbers_ByCountingFromLarger;
  //const addTwoNumbers = addTwoNumbers_UsingCarryArithmetic;
  const multiplyTwoNumbers = multiplyTwoNumbers_ByFactorSummation;
  //const multiplyTwoNumbers = multiplyTwoNumbers_FASTER;
  const convertToNumberSystem = convertToNumberSystem_ByCountingFromZero;
  //const convertToNumberSystem = convertToNumberSystem_FASTER;

/* Public Properties */

this.ZERO = DIGIT_ZERO;
  this.ONE = DIGIT_ONE;
  this.DIGITS = DIGITS;
  this.VALUES = VALUES;
  this.BASE = BASE;
  this.RADIX = RADIX;

/* Public Methods */

this.compare = function (m, n) {
    m = parseNumber(m);
    n = parseNumber(n);
    return compare(m, n);
  };

this.incrementByOne = function (n) {
    n = parseNumber(n);
    return incrementByOne(n).join(SEPARATOR);
  };

this.addTwoNumbers = function (m, n) {
    m = parseNumber(m);
    n = parseNumber(n);
    return addTwoNumbers(m, n).join(SEPARATOR);
  };

this.multiplyTwoNumbers = function (m, n) {
    m = parseNumber(m);
    n = parseNumber(n);
    return multiplyTwoNumbers(m, n).join(SEPARATOR);
  };

this.convertToNumberSystem = function (n, system) {
    n = parseNumber(n);
    return convertToNumberSystem(n, system).join(SEPARATOR);
  };

this.trimLeadingZeros = function (n) {
    n = parseNumber(n);
    return trimLeadingZeros(n).join(SEPARATOR);
  };

/* Finalization */

Object.freeze(this);

/* Private Utility Functions */

function getSeparator(config) {
    const separator = config.separator;
    if (typeof separator === "string") {
      return separator;
    }
    else {
      return "";
    }
  }

function getBase(digits) {
    const len = digits.length;
    if (len < 2) {
      throw Error("Not enough digits: " + len);
    }
    return len;
  }

function getZeroDigit(arrayOfDigits) {
    return arrayOfDigits[0];
  }

function getOneDigit(arrayOfDigits) {
    return arrayOfDigits[1];
  }

function getSubarray(a, lower, upper) {
    const sub = []
    for (let i = lower; i < upper; ++i) {
      sub.push(a[i]);
    }
    return Object.freeze(sub);
  }

function addTwoSingleDigitNumbers(n1, n2) {
    return addThreeSingleDigitNumbers(NUMBER_ZERO, n1, n2);
  }

function digitToNumber(digit) {
    return Object.freeze([digit]);
  }

function digitsToNumber(digits) {
    const length = digits.length;
    const number = [];
    for (let i = 0; i < length; ++i) {
      number[i] = digits[i];
    }
    return Object.freeze(number);
  }

function digitAt(number, index) {
    return number[index];
  }

function mostSignificantDigitOf(number) {
    return number[0];
  }

function leastSignificantDigitOf(number) {
    return number[number.length - 1];
  }

function trimLeadingZeros(n) {
    const upper = n.length;
    let lower = 0;
    while ((digitAt(n, lower) === DIGIT_ZERO) && (lower < upper)) {
      ++lower;
    }
    return getSubarray(n, lower, upper);
  }

function incrementByOne_ByAddingTwoNumbers(n) {
    return addTwoNumbers(n, NUMBER_ONE);
  }

function incrementByOne_Recursively(n) {
    const length = n.length;
    let left = length === 1 ? NUMBER_ZERO : getSubarray(n, 0, length - 1);
    const right = getSubarray(n, length - 1, length);
    const sum = addTwoSingleDigitNumbers(NUMBER_ONE, right);
    if (mostSignificantDigitOf(sum) === DIGIT_ONE) {
      left = incrementByOne(left);
    }
    return trimLeadingZeros(left.concat(leastSignificantDigitOf(sum)));
  }

function areEqual(m, n) {
    return compare(m, n) === 0;
  }

function isGreaterThan(m, n) {
    return compare(m, n) > 0;
  }
  function isGreaterThanOrEqual(m, n) {
    return compare(m, n) >= 0;
  }

function isLessThan(m, n) {
    return compare(m, n) < 0;
  }

function isLessThanOrEqual(m, n) {
    return compare(m, n) <= 0;
  }

function convertToNumberSystem_ByCountingFromZero(n, numberSystem) {
    let mAsString = numberSystem.ZERO;
    let count = NUMBER_ZERO;
    while (isLessThan(count, n)) {
      count = incrementByOne(count);
      mAsString = numberSystem.incrementByOne(mAsString);
    }
    return mAsString.split(SEPARATOR);
  }

}
</script>

Pages

Positional Number System

Positional Number System 1

Position Number System 2

Source Code