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:
Understand the problem
Make a plan
Execute the plan
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
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
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
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
🙄
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
The quotient is 1.
And what about modulo?
2 % 2
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
What do we do here? This isn't a binary value:
"1.5" + "1" = "1.51"
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
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:
_ _ _
What's the remainder of 5 divided by 2?
5 % 2 = 1
We prepend 1 to our string:
_ _ 1
Following the pseudocode we outlined above, we need to:
SET quotient EQUAL TO THE FLOOR OF decimal DIVIDED BY 2
But the result of that process is not a 1 or a 0:
5 / 2 = 2
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
So we prepend our string with 0:
_ 0 1
And divide 2 by 2:
2 / 2 = 1
And prepend our string with 1:
1 0 1
| 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
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('');
}
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)
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('');
}
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);
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
💯 Give yourself an A. Grab your copy of A is for Algorithms
Top comments (0)