Converting large numbers from binary to decimal and back in JavaScript

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I have a very large number represented as binary in JavaScript:

 var largeNumber = '11010011010110100001010011111010010111011111000010010111000111110011111011111000001100000110000011000001100111010100111010101110100010001011010101110011110000011000001100000110000011001001100000110000011000001100000110000111000011100000110000011000001100000110000011000010101100011001110101101001100110100100000110000011000001100000110001001101011110110010001011010001101011010100011001001110001110010100111011011111010000110001110010101010001111010010000101100001000001100001011000011011111000011110001110111110011111111000100011110110101000101100000110000011000001100000110000011010011101010110101101001111101001010010111101011000011101100110010011001001111101'

When I convert it to decimal by use of parseInt(largeNumber, 10)l it gives me 1.5798770299367407e+199 but when I try to convert it back to binary:

parseInt(`1.5798770299367407e+199`, 2)

it returns 1 (which I think is related to how parseInt works by rounding value) when I was expecting to see my original binary representation of largeNumber. Can you explain me such behavior? And how I can convert it back to original state in JavaScript?

EDIT: This question is a result of my experiment where I was playing around with storing and transferring large amount of boolean data. The largeNumber is a representation of a collection [true,true,false,true ...] of boolean values which has to be shared between client, client worker and server.

When you convert it back to binary, you don't parse it as base 2, that's wrong. You're also trying to parse an integer as a float, this can cause imprecision. With this line:

parseInt(`1.5798770299367407e+199`, 2)

You're telling JS to parse a base 10 as base 2! What you need to do is convert it to binary like so (note the use of parseFloat):

var largeNumber = '11010011010110100001010011111010010111011111000010010111000111110011111011111000001100000110000011000001100111010100111010101110100010001011010101110011110000011000001100000110000011001001100000110000011000001100000110000111000011100000110000011000001100000110000011000010101100011001110101101001100110100100000110000011000001100000110001001101011110110010001011010001101011010100011001001110001110010100111011011111010000110001110010101010001111010010000101100001000001100001011000011011111000011110001110111110011111111000100011110110101000101100000110000011000001100000110000011010011101010110101101001111101001010010111101011000011101100110010011001001111101';

//intLN is integer of large number
var intLN = parseFloat(largeNumber, 2); //here, you used base 10 to parse as integer, Incorrect
console.log(intLN);

var largeNumberConvert = intLN.toString(2); //here, we convert back to binary with toString(radix).
console.log(largeNumberConvert);

JavaScript Math: Convert a binary number to a decimal number , JavaScript exercises, practice and solution: Write a JavaScript function to convert a binary number to a decimal number. Convert Binary to Decimal In JavaScript. Convert a binary number to a decimal number using JavaScript will be easiest for us if we use. parseInt (); This method can take two parameters. In the first parameter, we can pass any string. So we can pass number string and this method will convert the string to a number. Just like this one: If we pass “1457” this method will convert it into a number like 1457. Now, In the second parameter, we can pass the base. That means in which number system

As noted in Andrew L.'s answer, and by several commenters, your largeNumber exceeds what JavaScript can represent as an integer in an ordinary number without loss of precision—which is 9.007199254740991e+15.

If you want to work with larger integers, you will need a BigInt library or other special-purpose code.

Below is some code demonstrating how to convert arbitrarily large positive integers between different base representations, showing that the exact decimal representation of your largeNumber is

15 798 770 299 367 407 029 725 345 423 297 491 683 306 908 462 684 165 669 735 033 278 996 876 231 474 309 788 453 071 122 111 686 268 816 862 247 538 905 966 252 886 886 438 931 450 432 740 640 141 331 094 589 505 960 171 298 398 097 197 475 262 433 234 991 526 525

function parseBigInt(bigint, base) {
  //convert bigint string to array of digit values
  for (var values = [], i = 0; i < bigint.length; i++) {
    values[i] = parseInt(bigint.charAt(i), base);
  }
  return values;
}

function formatBigInt(values, base) {
  //convert array of digit values to bigint string
  for (var bigint = '', i = 0; i < values.length; i++) {
    bigint += values[i].toString(base);
  }
  return bigint;
}

function convertBase(bigint, inputBase, outputBase) {
  //takes a bigint string and converts to different base
  var inputValues = parseBigInt(bigint, inputBase),
    outputValues = [], //output array, little-endian/lsd order
    remainder,
    len = inputValues.length,
    pos = 0,
    i;
  while (pos < len) { //while digits left in input array
    remainder = 0; //set remainder to 0
    for (i = pos; i < len; i++) {
      //long integer division of input values divided by output base
      //remainder is added to output array
      remainder = inputValues[i] + remainder * inputBase;
      inputValues[i] = Math.floor(remainder / outputBase);
      remainder -= inputValues[i] * outputBase;
      if (inputValues[i] == 0 && i == pos) {
        pos++;
      }
    }
    outputValues.push(remainder);
  }
  outputValues.reverse(); //transform to big-endian/msd order
  return formatBigInt(outputValues, outputBase);
}

var largeNumber =
  '1101001101011010000101001111101001011101' + 
  '1111000010010111000111110011111011111000' +
  '0011000001100000110000011001110101001110' +
  '1010111010001000101101010111001111000001' +
  '1000001100000110000011001001100000110000' +
  '0110000011000001100001110000111000001100' +
  '0001100000110000011000001100001010110001' +
  '1001110101101001100110100100000110000011' +
  '0000011000001100010011010111101100100010' +
  '1101000110101101010001100100111000111001' +
  '0100111011011111010000110001110010101010' +
  '0011110100100001011000010000011000010110' +
  '0001101111100001111000111011111001111111' +
  '1000100011110110101000101100000110000011' +
  '0000011000001100000110100111010101101011' +
  '0100111110100101001011110101100001110110' +
  '0110010011001001111101';

//convert largeNumber from base 2 to base 10
var largeIntDecimal = convertBase(largeNumber, 2, 10);


function groupDigits(bigint){//3-digit grouping
  return bigint.replace(/(\d)(?=(\d{3})+$)/g, "$1 ");
}

//show decimal result in console:
console.log(groupDigits(largeIntDecimal));

//converting back to base 2:
var restoredOriginal = convertBase(largeIntDecimal, 10, 2);

//check that it matches the original:
console.log(restoredOriginal === largeNumber);

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BigInt is built into js

function parseBigInt(str, base=10) {
  base = BigInt(base)
  var bigint = BigInt(0)
  for (var i = 0; i < str.length; i++) {
    var code = str[str.length-1-i].charCodeAt(0) - 48; if(code >= 10) code -= 39
    bigint += base**BigInt(i) * BigInt(code)
  }
  return bigint
}
parseBigInt('11010011010110100001010011111010010111011111000010010111000111110011111011111000001100000110000011000001100111010100111010101110100010001011010101110011110000011000001100000110000011001001100000110000011000001100000110000111000011100000110000011000001100000110000011000010101100011001110101101001100110100100000110000011000001100000110001001101011110110010001011010001101011010100011001001110001110010100111011011111010000110001110010101010001111010010000101100001000001100001011000011011111000011110001110111110011111111000100011110110101000101100000110000011000001100000110000011010011101010110101101001111101001010010111101011000011101100110010011001001111101', 2)
// 15798770299367407029725345423297491683306908462684165669735033278996876231474309788453071122111686268816862247538905966252886886438931450432740640141331094589505960171298398097197475262433234991526525n

Numbers, The same is true for most large numbers. Binary and octal numeral systems are rarely used, but also supported using the 0b and 0o prefixes:. Converting binary integer to decimal # To convert binary integer to decimal, start from the left. Take your current total, multiply it by two and add the current digit. Continue until there are no more digits left.Here is an example of such conversion using the fraction 1011.

If you're looking to transfer a large amount of binary data, you should use BigInt. BigInt allows you to represent an arbitrary number of bits.

// parse large number from string
let numString = '1101001101011010000101001111101001011101111100001001'

// as number
let num = BigInt('0b' + numString)

// now num holds large number equivalent to numString
console.log(num)  // 3718141639515913n

// print as base 2
console.log(num.toString(2))  // 1101001101011010000101001111101001011101111100001001

Helper functions

// some helper functions

// get kth bit from right
function getKthBit(x, k){
  return (x & (1n << k)) >> k;
}

// set kth bit from right to 1
function setKthBit(x, k){
  return (1n << k) | x;
}

// set kth bit from right to 0
function unsetKthBit(x, k){
  return (x & ~(1n << k));
}

getKthBit(num, 0n);  
// 1n

getKthBit(num, 5n);  
// 0n

setKthBit(num, 1n).toString(2); 
// 1101001101011010000101001111101001011101111100001011

setKthBit(num, 4n); 
// 1101001101011010000101001111101001011101111100011001

unsetKthBit(num, 0n).toString(2);
// 1101001101011010000101001111101001011101111100001000

unsetKthBit(num, 0n).toString(2);
// 1101001101011010000101001111101001011101111100000001

For convenience you may want to add this to BigInt if you're going to be serializing back to the client. Then you can read it back as a string. Otherwise you will get "Uncaught TypeError: Do not know how to serialize a BigInt" because for some reason Javascript Object Notation doesn't know how to serialize one of the types in Javascript.

    Object.defineProperty(BigInt.prototype, "toJSON", {
        get() {
            "use strict";
            return () => this.toString() + 'n';
        }
    });

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Program for Binary To Decimal Conversion, HTML � CSS � JavaScript � PHP � JQuery The idea is to extract the digits of given binary number starting from right most digit and keep a variable dec_value. C++ program to convert binary to decimal In case you want to work with long binary numbers like 20 bits or 30 bit, you can use string variable to� If you don't have a calculator to hand, you can easily convert a decimal number to binary using the remainder method. This involves dividing the number by 2 recursively until you're left with 0, while taking note of each remainder. Write down the decimal number. Divide the number by 2. Write the result underneath.

Converting larger number from decimal to binary (video), Converting larger number from decimal to binary. Transcript 0:34We can once again just Duration: 4:12 Posted: 9 Jul 2020 The table above shows the decimal number 122 broken down into binary. The process for converting from decimal to binary is described below. The left column contains the decimal number that will be divided by two. The middle column contains the integer result of the left column divided by two, minus any remainders.

The simple math behind decimal-binary conversion algorithms , If you search the web for "How to convert from decimal to binary" you will find that will allow you to convert binary numbers to decimal and back. Let's think of how big the sum of these numbers can be. javascriptbinary. Big number converter : This service allows you to convert big positive integer numbers into binary, decimal, hexadecimal or base64 encoding schemes. The big number bitsize is also calculated. For example: The following hexadecimal big number converted into a decimal encoding scheme: b5 6c 4f ee ef 1b 04 5d be 70 4a d8 55 1d 8a 77

Comments
  • parseInt isn't a method of converting from one number system to another. You need to go read what it actually does, then rethink how you achieve your end result.
  • "I have a very large number represented as binary" How was original number converted to largeNumber?
  • Converting a numerical string to a number is not a lossless process. Numbers only have 64 bits, they can't store much information.
  • This is a collection of boolean values which is a result of my experiment. I was trying to store the array of boolean as a binary number and convert them to decimal number to see if I can do that process more memory efficient
  • Have you considered included your description of actual requirement and expected result at Question? It may be helpful in resolving actual requirement? Was not certain what you were actually trying to achieve before reading your comment at stackoverflow.com/questions/39334494/…
  • largeNumber is too large for this.
  • The other subtlety here is negative numbers: stackoverflow.com/questions/9939760/…
  • @IanGilroy Yes, that's another thing to take into account
  • @guest271314 It doesn't. This is because the binary number is too large for JS, see last part of answer
  • "telling JS to parse a base 10 as base 2!" - actually it's worse than that. He's telling to parse a floating-point number in scientific notation as an integer.
  • This worked perfectly for my need. I just have a large binary string I have to convert to a decimal string
  • Note that with BigInt, the OP can be solved with the single expression BigInt('0b' + str).