One Pager Cheat Sheet

• Today's task involves writing a function that converts a decimal number to its binary representation; it requires understanding the definitions of binary and decimal, with the added constraints that the input will be a positive integer between 0 and 1000000000, and the expected time and space complexities are O(log n) and O(1) respectively.
• The article provides steps to convert a decimal number to binary, using the division with remainder method, by repeatedly dividing by 2 and recording the remainders, which, when read from bottom to top, give the binary representation of the original decimal number.
• The process of converting a decimal number to binary works by repeatedly dividing the decimal number by 2 and recording the remainder, symbolizing the sum of powers of 2 that construct the original decimal number, yielding the binary representation.
• The text outlines a coding approach to convert decimal numbers to binary, specifying that if a number is less than 1, an empty string should be returned and detailing two cases: if num is divisible by 2, and if it's not, whereby recursive operations are performed; the time and space complexity of this approach is O(logn).

This is our final solution.

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}

var assert = require('assert');

​

function decimalToBinary(num) {

  if (num >= 1) {

    if (num % 2) {

      return decimalToBinary((num - 1) / 2) + 1;

    } else {

      return decimalToBinary(num / 2) + 0;

    }

  } else {

    return '';

  }

}

​

try {

  assert.equal(decimalToBinary(3), 11);

​

  console.log('PASSED: ' + 'decimalToBinary(3) should return 11');

} catch (err) {

  console.log(err);

}

​

try {

  assert.equal(decimalToBinary(8), 1000);

​

  console.log('PASSED: ' + 'decimalToBinary(8) should return 1000');

} catch (err) {

  console.log(err);

}

​

try {

  assert.equal(decimalToBinary(1000), 1111101000);

Great job getting through this. Let's move on.

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