Decimal to hex converter

The hexadecimal number system (hex) is a base-16 positional numeral system widely used in programming, web development, and computer technologies. Unlike the familiar decimal system that uses digits 0-9, hexadecimal uses symbols 0-9 and letters A-F to represent numbers.

Hexadecimal System Basics

Hex symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, where A=10, B=11, C=12, D=13, E=14, F=15 in decimal.

How it works: Each position in a hexadecimal number represents a power of 16. For example, 1A3₁₆ = 1×16² + A×16¹ + 3×16⁰ = 256 + 160 + 3 = 419₁₀

Decimal to Hex Conversion Algorithm

• Divide the source number by 16
• Record the remainder (if remainder > 9, replace with corresponding letter A-F)
• Divide the quotient by 16 again
• Repeat until quotient equals 0
• Write all remainders in reverse order

Practical Conversion Examples

Example 1: 255₁₀ to hex
255 ÷ 16 = 15 remainder 15 (F)
15 ÷ 16 = 0 remainder 15 (F)
Result: FF₁₆

Example 2: 1000₁₀ to hex
1000 ÷ 16 = 62 remainder 8
62 ÷ 16 = 3 remainder 14 (E)
3 ÷ 16 = 0 remainder 3
Result: 3E8₁₆

Programming Applications

Hexadecimal system is widely used in:

• Web Design: CSS color codes (#FF5733)
• Programming: memory address representation
• Cryptography: hashing and encryption
• Debugging: machine code viewing
• Networking: MAC addresses

Advantages of Hex System

• Compact representation of large numbers
• Easy conversion to binary system
• Convenient for working with bytes (1 byte = 2 hex symbols)
• Industry standard in IT