Converting Between Number Systems

Computing uses multiple number systems. This guide shows you how to convert between decimal, hexadecimal, binary, and octal.

Number System Basics

System	Base	Digits Used
Decimal	10	0-9
Hexadecimal	16	0-9, A-F
Binary	2	0, 1
Octal	8	0-7

Decimal to Hexadecimal

To convert decimal to hexadecimal:

1. Divide the number by 16
2. Record the remainder (this becomes a hex digit)
3. Divide the quotient by 16
4. Repeat until quotient is 0
5. Read remainders from bottom to top

Example: Convert 255 to hex

• 255 ÷ 16 = 15 remainder 15 (F)
• 15 ÷ 16 = 0 remainder 15 (F)
• Result: FF

Hexadecimal to Decimal

Multiply each digit by 16 raised to its position power:

Example: Convert 1A3 to decimal

• 1 × 16² = 256
• A × 16¹ = 160
• 3 × 16⁰ = 3
• Total: 419

Binary to Hexadecimal

Group binary digits in sets of 4 (from right to left) and convert each group:

Example: Convert 11010110 to hex

• 1101 = D
• 0110 = 6
• Result: D6

Hexadecimal to Binary

Convert each hex digit to its 4-bit binary equivalent:

Example: Convert 3F to binary

• 3 = 0011
• F = 1111
• Result: 00111111

Practice Tips

1. Start Small: Practice with small numbers first
2. Verify: Convert back to check your work
3. Use Tools: Our calculator can verify your conversions
4. Memorize: Learn common hex values (0-F = 0-15)

Conclusion

Converting between number systems becomes easier with practice. Use our hex calculator to check your work and build confidence.