Binary Numbers in JavaScript

A binary number is a numerical system having a basis, or radix, of two in terms of number systems. This indicates that all values are represented by just the two numbers, 0 and 1. A "bit" is the abbreviation for a binary digit, which is each digit in a binary integer. Similar to the decimal system we use on a daily basis, binary is a positional number system that employs powers of two rather than powers of ten.

Binary numbers encode information in computer science using just two digits: 0 and 1. Since electrical circuits can be readily built to have two stable states, high voltage (commonly represented by 1) and low voltage (typically represented by 0), this system is essential to the operation of all modern computers.

Here are some essential details about binary numbers:

As a base-2 number system, binary bases the value of each digit on both its position and a base of two. The 1 (2^0) is indicated by the number farthest to the right, the 2 (2^1) by the digit immediately to the left, and so on.
Binary digits are used on computers to represent many types of data, including text, images, numbers, and even software. Each data point consists of a sequence of 1s and 0s.
The acronym bit represents any one of the binary digits. A single bit may store only two values, 0 and 1.
Bit groups: Groups of eight bits are utilized to represent a larger variety of values and are sometimes referred to as bytes.

Computers process information using binary digits as their base. Understanding the notion is crucial for anybody interested in computer science or the operation of digital equipment, even if it may need to be more intuitive to humans.

Here is an example to demonstrate how we count in binary number system notation. The table below shows the binary representation of decimal numbers 1 to 10.

Decimal Numbers	Binary Representation
1	0000
2	0001
3	0010
4	0011
5	0100
6	0101
7	0110
8	0111
9	1000
10	1010

Binary in JavaScript

In JavaScript, by default if we assign a number literal to a variable, it is considered as a decimal number(base10).

Code:

const a = 10;
console.log(a); // 10

In the above example, a contains decimal 10. It is not the binary equivalent of 2. In ES5, there is no way to represent a binary number. From ES6, to specify a binary number, we must prefix it with a leading zero followed by a lowercase or uppercase letter "B".

Code:

// ES6+
const a = 0b10;
console.log(a); // 2

const b = 0B10;
console.log(b); // 2

JavaScript engine treats a number as binary if it sees a 0b or 0B prefix.

If we use a number other than 0 and 1 after the prefix 0b or 0B, we get a Syntax Error.

Code:

Number System Conversions

There are various number systems, namely hexadecimal, decimal, octal, and binary. Each of these number systems is useful in particular tasks. Interconversion of these numbers is crucial. In this section, we will discuss the interconversion between binary and decimal.

Decimal to Binary Conversion:

We continually divide a decimal value by two and record the remainder to convert it to binary. Reading the remainders in reverse order yields the binary representation.

Algorithm:

25 ÷ 2 = 12 remainder 1

12 ÷ 2 = 6 remainder 0

6 ÷ 2 = 3 remainder 0

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1

Reading the remainders in reverse order, we get the binary representation: 11001.

Other than this, we will also see a javascript program to convert a decimal number to binary.

Code 1: Using toString() method

function decimalToBinary(decimal) {
    let binaryString = "";
    let remainder;
    // Loop until the decimal number becomes 0
    while (decimal > 0) {
      // Get the remainder of the division by 2
      remainder = decimal % 2;
      // Prepend the remainder (0 or 1) to the binary string
      binaryString = remainder + binaryString;
      // Divide the decimal number by 2 (integer division)
      decimal = Math.floor(decimal / 2);
    }
  
    return binaryString;
  } 
console.log(decimalToBinary(5));  

Output:

Code 2: Using Bit Manipulation

function decimalToBinary(decimal) {
  let binaryString = "";
  let remainder;

  // Loop until the decimal number becomes 0
  while (decimal > 0) {
    // Get the remainder of the division by 2
    remainder = decimal % 2;
    // Prepend the remainder (0 or 1) to the binary string
    binaryString = remainder + binaryString;
    // Divide the decimal number by 2 (integer division)
    decimal = Math.floor(decimal / 2);
  }

  return binaryString;
}

console.log(decimalToBinary(5));  

Output:

Conclusion

In conclusion, this article covers the significance of binary numbers in general number systems and computer science. It describes how binary, which is essential for encoding digital data, represents values using 0 and 1 digits. It also covers bit manipulation and tools like toString() for converting decimal integers to binary.

Next TopicComparing Arrays in JavaScript

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