Octal and Binary Literals

JavaScript supports octal and binary literals for working with numbers in octal (base-8) and binary (base-2) formats. This can be helpful when dealing with certain types of numerical data, such as file permissions, binary data, bitwise operations, and low-level system programming.

In this tutorial, we will explore how to use octal and binary literals in JavaScript with several code examples.

1. Octal Literals

An octal literal is a number represented in base-8. In JavaScript, octal literals use a leading 0o or 0O (zero followed by a lowercase or uppercase “O”).

Syntax

let octalNumber = 0o[number];

The 0o prefix indicates that the number is in octal format.
[number] is a sequence of digits from 0 to 7.

Example 1: Basic Octal Literals

let octal1 = 0o10; // Octal 10 (base 8)
let octal2 = 0o77; // Octal 77 (base 8)

console.log(octal1); // Output: 8 (decimal)
console.log(octal2); // Output: 63 (decimal)

Explanation

0o10 represents the octal number 10, which equals 8 in decimal.
0o77 represents the octal number 77, which equals 63 in decimal.

Example 2: Using Octal Literals for Permissions

Octal literals are often used in programming environments to represent file permissions, as in Unix-based systems.

let readWriteExecute = 0o777; // Full permissions
let readOnly = 0o444; // Read-only permissions

console.log(readWriteExecute); // Output: 511 (decimal)
console.log(readOnly); // Output: 292 (decimal)

Explanation

0o777 represents full permissions (rwxrwxrwx), which converts to 511 in decimal.
0o444 represents read-only permissions (r–r–r–), which converts to 292 in decimal.

Example 3: Invalid Octal Literals

Octal literals can only contain digits from 0 to 7. Using digits outside this range will result in a syntax error.

// let invalidOctal = 0o89; // SyntaxError: Invalid or unexpected token

Explanation

Octal numbers can only have digits from 0 to 7. Including 8 or 9 in an octal literal will cause an error.

2. Binary Literals

A binary literal is a number represented in base-2. In JavaScript, binary literals use a leading 0b or 0B (zero followed by a lowercase or uppercase “B”).

Syntax

let binaryNumber = 0b[number];

The 0b prefix indicates that the number is in binary format.
[number] is a sequence of 0s and 1s.

Example 4: Basic Binary Literals

let binary1 = 0b1010; // Binary 1010 (base 2)
let binary2 = 0b1111; // Binary 1111 (base 2)

console.log(binary1); // Output: 10 (decimal)
console.log(binary2); // Output: 15 (decimal)

Explanation

0b1010 represents the binary number 1010, which equals 10 in decimal.
0b1111 represents the binary number 1111, which equals 15 in decimal.

Example 5: Using Binary Literals in Bitwise Operations

Binary literals are commonly used in bitwise operations, which operate directly on binary digits of integers.

let mask = 0b0101; // Binary 0101 (decimal 5)
let number = 0b1010; // Binary 1010 (decimal 10)

let result = number & mask; // Bitwise AND operation

console.log(result.toString(2)); // Output: 0 (binary) since there are no matching '1's

Explanation

0b0101 and 0b1010 are binary numbers.
The & (bitwise AND) operation compares each bit and returns 1 if both bits are 1. In this case, the result is 0.

Example 6: Invalid Binary Literals

Binary literals can only contain 0s and 1s. Using other digits will result in a syntax error.

// let invalidBinary = 0b102; // SyntaxError: Invalid or unexpected token

Explanation

Binary numbers can only have digits 0 and 1. Including any other digits in a binary literal will cause an error.

3. Conversions Between Binary, Octal, and Decimal

JavaScript provides built-in methods to convert numbers between binary, octal, and decimal.

Example 7: Converting Decimal to Binary and Octal

You can use the toString() method to convert a number to binary or octal format.

let number = 42;

let binary = number.toString(2); // Convert to binary
let octal = number.toString(8); // Convert to octal

console.log(binary); // Output: "101010"
console.log(octal); // Output: "52"

Explanation

number.toString(2) converts the decimal number 42 to binary (“101010”).
number.toString(8) converts the decimal number 42 to octal (“52”).

Example 8: Parsing Binary and Octal Strings

You can use parseInt() to convert a binary or octal string to a decimal number.

let binaryString = '1010';
let octalString = '52';

let binaryNumber = parseInt(binaryString, 2); // Parse as binary
let octalNumber = parseInt(octalString, 8); // Parse as octal

console.log(binaryNumber); // Output: 10
console.log(octalNumber); // Output: 42

Explanation

parseInt(binaryString, 2) converts the binary string “1010” to its decimal equivalent (10).
parseInt(octalString, 8) converts the octal string “52” to its decimal equivalent (42).

4. Real-world Applications of Binary and Octal Literals

Example 9: Setting Permissions with Octal Literals

Octal literals are useful when setting file permissions, commonly used in Unix-like operating systems.

let readWriteExecute = 0o755; // rwxr-xr-x
let readWriteOnly = 0o644; // rw-r--r--

console.log(readWriteExecute); // Output: 493
console.log(readWriteOnly); // Output: 420

Example 10: Using Binary for Flag Management

Binary literals are often used in low-level programming for flag management.

let FLAG_READ = 0b0001; // 1
let FLAG_WRITE = 0b0010; // 2
let FLAG_EXECUTE = 0b0100; // 4

// Combining flags using bitwise OR
let permissions = FLAG_READ | FLAG_WRITE;

console.log(permissions.toString(2)); // Output: "11" (binary)

Explanation

This example uses binary literals to define flags and combines them using the bitwise OR (|) operation.

Summary

JavaScript's support for octal (0o) and binary (0b) literals makes it easier to work with non-decimal numeric systems, which can be helpful in various programming scenarios, such as file permissions and low-level bitwise operations.

Quick Reference

Common Uses

• Octal Literals: Useful for file permissions and other numeric codes in systems programming.
• Binary Literals: Helpful for bitwise operations, flag management, and working with binary data.

By mastering these literals, you can write more expressive and understandable JavaScript code when dealing with different numeric systems.