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Bitwise in JavaScript

This project aims to provide educational resources on bitwise operations in JavaScript. Explore practical examples and fundamental concepts to understand how bitwise can be applied in development.

What is a bit?

A bit is the fundamental unit of information in computers and represents the smallest data element in a digital system.

Value of a bit

The value of a bit can vary between 0 and 1.

What is a binary?

A binary is a set of bits. We can say that the binary with 4 bits 0010 is 2

Decimal to Binary

There are several ways to convert a decimal to binary, but below I leave some techniques to make it easier.

• First Technique

Let's start with a simple number, for example 1

1÷2 which will have 1 as remainder and 0 as quotient.

With the calculation above we can say that the remainder is the binary representation. In a 4-bit binary we can say that decimal 1 is represented as 0001.

Now let's try number 13.

13/2 which will have 1 as remainder and 6 as quotient.

6/2 which will have 0 as remainder and 3 as quotient.

3/2 which will have 1 as remainder and 1 as quotient.

1/2 which will have 1 as remainder and 0 as quotient.

So the decimal of 13 in a 4-bit binary would be 1101

• Second Technique

256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1

Taking the examples of numbers from the first technique, let's start with the number 1.

We take the list of numbers above and add the numbers together until we get the decimal.

In the case of 1 we will only need 1 so I put a (1) in 1. So in a 4-bit binary we can say that the decimal of 1 is represented by 0001

256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1(1)

Now taking number 13

256 | 128 | 64 | 32 | 16 | 8(8) | 4(12) | 2 | 1(1)

Following this logic we can add until we complete 13 (8+4+1)

So the order would be 1101 taking into account that where it was not necessary to add we put 0

Operators

Name	OR	AND	XOR	NOT	Left Shift	Right Shift
Symbol	|	&	^	~	<<	>>

OR

The OR operator is represented by the symbol | and is used to compare two binary values. If either value is 1, the result is 1. If both values are 0, the result is 0.

Example

let num1 = 1; // 0001
let num2 = 10; // 1010

/*
     0 0 0 1
     1 0 1 0

     1 0 1 1
*/

let result = num1 | num2;

console.log(result); // 11 (1011)

AND

The AND operator is represented by the symbol & and is used to compare two binary values. If both values are 1, the result is 1. If either value is 0, the result is 0.

Example

     let num1 = 1; // 0001
     let num2 = 10; // 1010

     let all = num1 | num2; // 11 (1011)

     /*
         0 0 0 1
         1 0 1 1

         0 0 0 1
     */

     let result = all & num1; // 1 (0001)

     if (result) {
         console.log('Number 1 is present'); // this scope will be executed
     }

XOR

The XOR operator is represented by the symbol ^ and is used to compare two binary values. If both values are 1 or 0, the result is 0. If one of the values is 1 and the other 0, the result is 1.

Example

     let num1 = 1; // 0001
     let num2 = 10; // 1010

     /*
         0 0 0 1
         1 0 1 0

         1 0 1 1
     */

     let result = num1 ^ num2; // 11 (1011)

     console.log(result); // 11 (1011)

NOT

The NOT operator is represented by the symbol ~ and is used to invert the value of a binary. If the value is 1, the result will be 0. If the value is 0, the result will be 1.

Example

     let num1 = 1; // 0001

     /*
         0 0 0 1

         1 1 1 0
     */

     let result = ~num1;

     console.log(result); // 14 (1110)

Left Shift

The Left Shift operator is represented by the symbol << and is used to move bits to the left. The value of the leftmost bit is discarded and a 0 is added to the right. The value of the rightmost bit is discarded.

Example

     let num1 = 1; // 0001

     /*
         0 0 0 1

         0 0 1 0
     */

     let result = num1 << 1;

     console.log(result); // 2 (0010)

Right Shift

The Right Shift operator is represented by the symbol >> and is used to move bits to the right. The value of the rightmost bit is discarded and a 0 is added to the left. The value of the leftmost bit is discarded.

Example

     let num1 = 1; // 0001

     /*
         0 0 0 1

         0 0 0 0
     */

     let result = num1 >> 1;

     console.log(result); // 0 (0000)

Practical examples

The examples are in the folder examples

Contribute

If you would like to contribute to this project, please read CONTRIBUTING.md for details on our code of conduct and process