# Encoding a number string into a string of 0s and 1s in JavaScript

## Problem

We are required to write a JavaScript function that takes in a string that represents a decimal number.

Our function should convert/encode this decimal into binary based on the following rules.

For each digit d of n

• Let k be the number of bits of d
• We write k-1 times the digit 0 followed by the digit 1
• We write digit d as a binary string, with the rightmost bit being the least significant
• Lastly, we concatenate the result of b) and c) to get the coding of d

At last, we concatenate all the results got for the digits of n.

Thus, code 2 as 0110 and 3 as 0111

## Example

Following is the code −

const str = '77338855';
const encodeNumString = (str = '') => {
const buildarray = (string = '') => {
let n = string.split(''), res = '';
n.forEach(x => {
let num = Number(x).toString(2);
num = '0'.repeat(num.length -1) + '1' + num;
res += num;
});
return res;
}
const arr = [];
let res = "";
for (let i = 0; i < 10; i++){
arr.push(buildarray(String(i)));
};
while (str.length){
for (let i = 0; i < 10; i++) {
if (str.startsWith(arr[i])) {
res += String(i);
str = str.slice(arr[i].length);
break;
}
}
}
return res;
};
console.log(encodeNumString(str));

## Output

Following is the console output −

001111001111011101110001100000011000001101001101