DEV Community

Cover image for How to Convert Decimal to Binary in JavaScript and Python
Jared Nielsen
Jared Nielsen

Posted on • Originally published at jarednielsen.com

How to Convert Decimal to Binary in JavaScript and Python

If you want to learn how to code, you need to learn algorithms. Learning algorithms improves your problem solving skills by revealing design patterns in programming. In this tutorial, you will learn how to code a decimal to binary conversion algorithm in JavaScript and Python.

This post originally published at jarednielsen.com

How to Code a Decimal to Binary Algorithm

Programming is problem solving. There are four steps we need to take to solve any programming problem:

  1. Understand the problem

  2. Make a plan

  3. Execute the plan

  4. Evaluate the plan

Understand the Problem

To understand our problem, we first need to define it. Let’s reframe the problem as acceptance criteria:

GIVEN a decimal
WHEN I pass it to a function for conversion
THEN the function returns the binary equivalent
Enter fullscreen mode Exit fullscreen mode

That’s our general outline. We know our input conditions (a decimal) and our output requirements (a binary equivalent), and our goal is to perform the conversion of the decimal to binary.

Let’s make a plan!

Make a Plan

Let’s revisit our computational thinking heuristics as they will aid and guide is in making a plan. They are:

  • Decomposition

  • Pattern recognition

  • Abstraction

  • Algorithm

When we are decomposing a problem, we break the problem down into smaller problems that are easier to solve.

What's the smallest problem we can solve?

1

In base 10, what is 1?

It is one of ten possible values, or, 1 / 10.

In base 2, what is 1?

It is one of two possible values.

What mathematical operation do we use to break problems down?

Division.

If we're using division to convert to binary, what is our divisor?

2

What do we know about division?

The division operation divides one number, the dividend, by another number, the divisor, and returns a quotient and a remainder. So we're on the same page with terminology, let's look at an example...

3 / 2 = 1
Enter fullscreen mode Exit fullscreen mode

3 is the dividend, 2 is the divisor, and 1 is the quotient. What about the remainder? We use the modulo operator.

3 % 2 = 1
Enter fullscreen mode Exit fullscreen mode

Here, again, 3 is the dividend, 2 is the divisor, but the result of the modulo operation, the remainder, is 1.

Let's start simple and convert 0 to binary. What is the quotient of the following:

0 / 2
Enter fullscreen mode Exit fullscreen mode

🙄

It's 0.

So it's safe to say that the binary equivalent of the decimal 0 is also 0.

If we start to build a table, it looks like this so far:

Decimal Binary
0 0

Because we are only working with two values, 0 and 1, we can surmise that the decimal 1 converted to binary is also 1.

Decimal Binary
0 0
1 1

But don't take my word for it! Let's prove it.

What is 1 / 2?

0.5

Can we work with this?

It's not a whole number.

Our goal is to represent decimal values using only 1s and 0s. How do we accomplish this goal?

Use the remainder!

What is 1 % 2?

1

Let's map out the first five modulo operations J4F:

Modulo Remainder
0 % 2 0
1 % 2 1
2 % 2 0
3 % 2 1
4 % 2 0

See a pattern? When we perform the modulo operation using 2, the value returned will be either a 1 or a 0.

Now we need an approach to represent numbers greater than or equal to 2.

What happens when we divide 2 by 2?

2 / 2
Enter fullscreen mode Exit fullscreen mode

The quotient is 1.

And what about modulo?

2 % 2
Enter fullscreen mode Exit fullscreen mode

The remainder is 0. If we concatenate the quotient and the remainder, we get 10, the binary equivalent of 2.

Decimal Binary
0 0
1 1
2 10

Are you starting to see the pattern?

We're building our binary strings with the remainder, and not the quotient, of our division operation. We continue to perform the division operation while our number is greater than 0.

What about 3?

3 % 2 = 1
3 / 2 = 1.5
Enter fullscreen mode Exit fullscreen mode

What do we do here? This isn't a binary value:

"1.5" + "1" = "1.51"
Enter fullscreen mode Exit fullscreen mode

We need to round down, or floor it. 🏎️

Decimal Binary
0 0
1 1
2 10
3 11

Let's pseudocode our approach so far:

INPUT decimal

SET binary string EQUAL TO decimal MODULO 2
SET quotient EQUAL TO THE FLOOR OF decimal DIVIDED BY 2
PREPEND binary string WTIH quotient

OUTPUT binary string
Enter fullscreen mode Exit fullscreen mode

What about 4?

You guessed it, we need to add another digit. Without calculating it, what is the binary equivalent of 4? Do you see a pattern emerging?

Decimal Binary
0 0
1 1
2 10
3 11
4 100

What about 5? Let's build a string! We're now working with three digits, so let's create three placeholders:

_ _ _
Enter fullscreen mode Exit fullscreen mode

What's the remainder of 5 divided by 2?

5 % 2 = 1
Enter fullscreen mode Exit fullscreen mode

We prepend 1 to our string:

_ _ 1
Enter fullscreen mode Exit fullscreen mode

Following the pseudocode we outlined above, we need to:

SET quotient EQUAL TO THE FLOOR OF decimal DIVIDED BY 2
Enter fullscreen mode Exit fullscreen mode

But the result of that process is not a 1 or a 0:

5 / 2 = 2
Enter fullscreen mode Exit fullscreen mode

Where have we seen something this or somthing like it before? 🤔

2!

The binary equivalent of 2 is 10. How did we get that?

2 % 2 = 0
Enter fullscreen mode Exit fullscreen mode

So we prepend our string with 0:

_ 0 1
Enter fullscreen mode Exit fullscreen mode

And divide 2 by 2:

2 / 2 = 1
Enter fullscreen mode Exit fullscreen mode

And prepend our string with 1:

1 0 1
Enter fullscreen mode Exit fullscreen mode
Decimal Binary
0 0
1 1
2 10
3 11
4 100
5 101

Let's update our pseudocode:

INPUT decimal

SET binary string TO EMPTY STRING

WHILE decimal IS GREATER THAN 0
    PREPEND THE RESULT OF decimal MODULO 2 TO binary string
    REASSIGN decimal THE FLOOR VALUE OF decimal DIVIDED BY 2

OUTPUT binary string
Enter fullscreen mode Exit fullscreen mode

Execute the Plan

Finally, we simply need to implement the design of our algorithm.

How to Code a Decimal to Binary Conversion in JavaScript

In our solution, rather than prepending each remainder, we instead concatenate the result string and use a combination of string and array methods to split the string into array items, reverse the order of the array, and then join the items in a string.

const decimalToBinary = (num) => {

    let result = '';

    while (num > 0){ 
      result += num % 2; 
      num = Math.floor(num / 2); 
    }

    return result.split('').reverse().join('');
}
Enter fullscreen mode Exit fullscreen mode

How to Code a Decimal to Binary Conversion in Python

Similar to above, we perform split, reverse, and join operations. Note that we don't need to import the math library as double division in Python will floor the returned value for us.

def decimal_binary(num):
    result = ''

    while num > 0:
        result += str(num % 2)
        num = num // 2

    result.split().reverse()

    return ''.join(result)
Enter fullscreen mode Exit fullscreen mode

Evaluate the Plan

Let's take another look at our JavaScript solution. The split() method converts the string to an array, so we could just start with an array instead and use unshift() rather than reverse() (J4F):

const decimalToBinary = (num) => {

  let result = [];

  while (num > 0){ 
    result.unshift(num % 2); 
    num = Math.floor(num / 2); 
  }

  return result.join('');
}
Enter fullscreen mode Exit fullscreen mode

Or we could just cheat and use the built-in toString() method and pass it 2 as an argument, meaning we want to convert our string to binary:

const decimalToBinary = num => num.toString(2);
Enter fullscreen mode Exit fullscreen mode

But what fun is that?

The same is true for Python. We can simply call the bin() method. But, this will prepend the string with 0b.

A is for Algorithms

Image description
💯 Give yourself an A. Grab your copy of A is for Algorithms

Top comments (0)