Converting Between Number Systems in JavaScript: A Complete Guide

Quick Tricks to Remember Number Conversions in JavaScript

Understanding how to convert between number systems is essential, but remembering the methods and bases can be tricky. To help you memorize and recall these conversions quickly, here’s a cheat sheet with tricks and a table format for easier recall.

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Quick Tips & Tricks

1. Use the .toString() Method for Decimal to Any Base

• Trick: Remember the number in toString(base) corresponds to the base you want to convert to.
  • Base 2: Binary
  • Base 8: Octal
  • Base 16: Hexadecimal
• Example: num.toString(2) converts to binary, num.toString(8) to octal, and num.toString(16) to hexadecimal.

1. Use parseInt() for Conversions to Decimal

• Trick: parseInt(num, base) is used to convert from binary, octal, or hexadecimal to decimal. The base tells JavaScript what format the number is in.
• Example: parseInt(binary, 2) converts binary to decimal, parseInt(octal, 8) for octal, and parseInt(hexa, 16) for hexadecimal.

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Conversion Table for Number Systems in JavaScript

Conversion	Method	Explanation	Example
Decimal to Binary	num.toString(2)	Converts decimal to binary	10.toString(2) → "1010"
Decimal to Octal	num.toString(8)	Converts decimal to octal	10.toString(8) → "12"
Decimal to Hexadecimal	num.toString(16)	Converts decimal to hexadecimal	10.toString(16) → "a"
Binary to Decimal	parseInt(binary, 2)	Converts binary to decimal	parseInt('1010', 2) → 10
Binary to Octal	parseInt(binary, 2).toString(8)	Converts binary to decimal, then decimal to octal	parseInt('1010', 2).toString(8) → "12"
Binary to Hexadecimal	parseInt(binary, 2).toString(16)	Converts binary to decimal, then decimal to hexadecimal	parseInt('1010', 2).toString(16) → "a"
Octal to Decimal	parseInt(octal, 8)	Converts octal to decimal	parseInt('12', 8) → 10
Octal to Binary	parseInt(octal, 8).toString(2)	Converts octal to decimal, then decimal to binary	parseInt('12', 8).toString(2) → "1010"
Octal to Hexadecimal	parseInt(octal, 8).toString(16)	Converts octal to decimal, then decimal to hexadecimal	parseInt('12', 8).toString(16) → "a"
Hexadecimal to Decimal	parseInt(hexa, 16)	Converts hexadecimal to decimal	parseInt('a', 16) → 10
Hexadecimal to Binary	parseInt(hexa, 16).toString(2)	Converts hexadecimal to decimal, then decimal to binary	parseInt('a', 16).toString(2) → "1010"
Hexadecimal to Octal	parseInt(hexa, 16).toString(8)	Converts hexadecimal to decimal, then decimal to octal	parseInt('a', 16).toString(8) → "12"

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Memory Aids

1. The Bases:

• Binary → Base 2 (Think of it as the smallest base, using only 0s and 1s).
• Octal → Base 8 (It’s 2³, so think of it as 3 sets of binary digits).
• Hexadecimal → Base 16 (Use digits 0-9 and letters a-f to represent values above 9).

1. Key Patterns:

• Binary (Base 2): Only uses 0 and 1.
• Octal (Base 8): Uses digits 0-7.
• Hexadecimal (Base 16): Uses digits 0-9 and letters a-f (with a = 10, b = 11, etc.).

1. Tip for Converting Between Bases:

• For Binary to Octal and Binary to Hexadecimal, you can group the binary digits in sets of 3 (for octal) or 4 (for hexadecimal). This makes it easier to convert without intermediate steps. Example:
• Binary to Octal: Group binary digits in sets of 3, from right to left.
  • Binary: 101011 → Group as 101 011 → Octal: 53.
• Binary to Hexadecimal: Group binary digits in sets of 4, from right to left.
  • Binary: 101011 → Group as 0010 1011 → Hexadecimal: 2b.

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Conclusion

By using these tricks and the conversion table, you can efficiently recall and apply the correct method for any number system conversion in JavaScript. Whether you’re dealing with binary, octal, decimal, or hexadecimal, these quick tips will help you navigate between them with ease! Keep this guide handy as a reference, and you’ll never get stuck with conversions again.