How To Convert Number To Binary In JavaScript

Binary number system is a base-2 number system that uses only two digits: 0 and 1. In computing, binary numbers are commonly used to represent information as it can be easily understood by electronic devices. JavaScript is a popular programming language that is widely used for web development.

It provides built-in methods to convert numbers to binary format, which can be useful in various scenarios such as manipulating data, performing bitwise operations, or working with binary-coded data.

Why is there a need to convert number to binary in javascript

Here are a few reasons why the conversion of numbers to binary is needed in Javascript.

1. Binary is a fundamental concept in computer science: In computer science, everything is ultimately represented in binary form. Therefore, being able to convert numbers to binary is important for understanding.
2. Bitwise operations: Binary numbers are often used in bitwise operations, such as bit shifting, AND, OR, XOR, and NOT operations.
3. Binary data transmission: In certain applications, data is transmitted in binary form, such as in networking protocols, file formats, and other forms of data exchange.

Different Approaches to convert number to binary in javascript

Here are some of the different approaches that how to convert a number to binary in javascript:

1. Using the Number.toString()
2. Using the bitwise operators
3. Using recursion

Method 1: Using Number.toString() method

One of the easiest and most common ways to convert a number to binary in JavaScript is by using the toString() method with a radix of 2. The radix parameter specifies the base of the number system to be used while converting a number to a string.

// Define a number to convert to binary
const num = 42;

// Use the toString() method with a radix of 2 to convert the number to a binary string
const binaryString = num.toString(2);

// Log the binary string to the console
console.log(binaryString);

Output:

101010

Explanation:

1. Define a decimal number 42 and store it in a variable called decimalNumber.
2. Use the toString() method on decimalNumber with a radix of 2 to convert it to a binary string.
3. Store the resulting binary string in a variable called binaryString.
4. Log binaryString to the console using the console.log() method.
5. When the code is executed, the binary representation of 42 (101010) is output to the console.

Method 2: Using Bitwise Operator method

Bitwise operators are operators that work on individual bits of numbers. By using bitwise operators, we can convert a decimal number to a binary number.

function decimalToBinary(num) {
  let binary = "";
  while (num > 0) {
    binary = (num & 1) + binary;
    num >>= 1;
  }
  return binary;
}

// Example usage
const num = 42;
const binary = decimalToBinary(num);
console.log(binary); 

Output:

101010

Explanation:

1. Inside the decimalToBinary function, we first initialize an empty string binary to hold the binary digits.
2. We then enter a while loop that continues as long as num is greater than zero.
3. Inside the loop, we use the bitwise AND operator & to get the value of the least significant bit (LSB) of num. The result will be either 0 or 1, depending on whether the LSB is a 0 or 1.
4. We concatenate the result to the beginning of the binary string.
5. We then use the bitwise right shift operator >>= to shift num one bit to the right, effectively removing the LSB.
6. The loop continues until num becomes zero, at which point we have converted the entire number to binary.
7. Finally, we return the binary string.

Method 3: Using recursion

Recursion is a programming technique where a function calls itself to solve a problem. In JavaScript, you can use recursion to convert a decimal number to binary.

function decimalToBinary(decimal) {
  if (decimal === 0) {
    return "0";
  } else if (decimal === 1) {
    return "1";
  } else {
    return decimalToBinary(Math.floor(decimal / 2)) + (decimal % 2).toString();
  }
}

// Example usage
console.log(decimalToBinary(13)); // Output: 1101
console.log(decimalToBinary(0)); // Output: 0

Output:

1101
0

Explanation:

1. Inside the decimalToBinary function, check if the input decimal is zero using the condition if (decimal === 0).
2. If the decimal is zero, return the string “0” as the binary equivalent.
3. If the decimal is not zero, check if it is one using the condition else if (decimal === 1).
4. If the decimal is one, return the string “1” as the binary equivalent.
5. If the decimal is not zero or one, use recursion to convert the integer part of decimal / 2 to binary by calling decimalToBinary again and concatenate the result with the remainder of decimal % 2 converted to a string using .toString().
6. Return the binary equivalent of the decimal number as a string.
7. To use the decimalToBinary function, call it with a decimal number as an argument, and it will return the binary equivalent of that number.

Best Approach to change a Number to binary in javascript

Here are some reasons why toString() method with a radix of 2 is the best approach:

1. It is simple and easy to use: The toString() method is a built-in method in JavaScript, and using a radix of 2 is a straightforward way to convert a number to binary.
2. It is efficient: The toString() method is optimized for performance, and it is a fast way to convert a number to a string in binary format.
3. It is widely supported: The toString() method with a radix parameter is supported in all modern browsers.

Sample Problems on Number to binary conversion in JavaScript.

Sample Problem 1:

Suppose you are making a function in which users enter their age and for privacy purposes you hide them with the help of converting numbers into binary in javascript.

Solution:

1. We define a function called convertAgeToBinary() that takes no arguments.
2. Inside the function, we prompt the user to enter their age using the prompt() method and store the result in a variable called age.
3. We then convert the age variable to a binary string using the Number() and toString() methods. The toString() method takes an optional argument that specifies the radix (or base) of the number system to use. In this case, we pass in 2 as the radix, which converts the number to binary.
4. We store the binary age string in a variable called binaryAge.
5. Finally, we log the binary age string to the console using a template literal.

Solution Code:

function hideAge() {
  // Ask user for their age
  const age = prompt("Please enter your age:");

  // Convert age to binary
  const binaryAge = parseInt(age).toString(2);
  // Display the binary age value to the user
  alert(`Your age in binary is: ${binaryAge}`);
}
hideAge();

Output

Please enter your age: 35
Your age in binary is: 100011

Sample Problem 2:

Suppose you are calculating a percentage of 800 out of 1500 and you need to convert from number to binary in javascript.

Solution:

1. First, we initialize two variables numerator and denominator with the values 800 and 1600 respectively.
2. Next, we calculate the percentage by dividing the numerator by the denominator and multiplying it by 100. The result is stored in the percentage variable.
3. To convert the percentage to binary, we use the unsigned right shift (>>>) bitwise operator. This operator shifts the bits of a number to the right and pads the left side with zeros. By shifting the percentage variable by 0 bits, we are essentially using this operator to force the number to be interpreted as an unsigned integer. We then convert the result to a binary string using the toString() method with a base of 2.
4. Finally, we print out the percentage and binary variables using the console.log() method.

let numerator = 800;

let denominator = 1600;

let percentage = (numerator / denominator) * 100; // calculating the percentage

let binary = (percentage >>> 0).toString(2); // converting to binary using bitwise operator

console.log("Percentage:", percentage); // Output: Percentage: 50

console.log("Binary:", binary); // Output: Binary: 110010

Output:

Percentage: 50
Binary: 110010

Sample Problem 3:

Suppose you are calculating HCF two numbers 65 and 95 and you want to convert that HCF into binary numbers.

Solution:

1. The find HCF function uses recursion to calculate the highest common factor of two numbers a and b.
2. It works by repeatedly dividing a by b and taking the remainder until b becomes zero. At this point, the value of a is the HCF.
3. The toBinary function uses recursion to convert a decimal number n to binary. It works by repeatedly dividing n by 2 and taking the remainder until n becomes zero. The binary representation is obtained by concatenating the remainder in reverse order.
4. In the main program, we call findHCF with arguments 65 and 95 to obtain the HCF. We then call toBinary with the HCF to obtain its binary representation.

function findHCF(a, b) {
  if(b == 0) {
    return a;
  } else {
    return findHCF(b, a % b);
  }
}

function toBinary(n) {
  if(n == 0) {
    return "0";
  } else if(n == 1) {
    return "1";
  } else {
    return toBinary(Math.floor(n/2)) + (n % 2).toString();
  }
}

// calculate HCF of 65 and 95
let hcf = findHCF(65, 95);
console.log("HCF of 65 and 95 is: ", hcf);

// convert HCF to binary
let binaryHCF = toBinary(hcf);
console.log("Binary representation of HCF is: ", binaryHCF);

Output:

HCF of 65 and 95 is:  5
Binary representation of HCF is:  101

Conclusion

In conclusion, converting a number to binary in JavaScript is a straightforward process that can be accomplished using a few lines of code.

By understanding the fundamentals of binary representation and the built-in methods in JavaScript, it’s possible to convert decimal numbers to binary with ease.