Decimal to Hex Converter

What Is the Decimal Number System?

The decimal number system uses ten digits, 0 to 9, and has base 10. Each digit has a place value based on powers of 10. We use it for everyday counting, prices, scores, measurements, and calculations in school and daily life every day.

What Is Hexadecimal?

Hexadecimal is a base 16 number system. It uses 0 to 9 and A to F, where A means 10 and F means 15. Computers use hex to write binary data in a shorter, easier form for code, memory values, and digital data used by programs.

How to Convert Decimal to Hex Manually

Decimal to hex uses repeated division by 16. The remainder becomes a hex digit. Use A to F for remainders 10 to 15.

Formula: $n = 16q + r$

Step by step Guide:

1. Divide the decimal number by 16.
2. Record the remainder.
3. Divide the quotient by 16.
4. Repeat until the quotient is 0.
5. Read remainders from bottom to top.

Practical Example: Convert 45 to hex. $45 \div 16 = 2$ remainder $13$. Then $2 \div 16 = 0$ remainder 2. Remainder 13 becomes D. Read 2 and D, so $45_{10} = 2D_{16}$.

Methods for Converting Decimal to Hex

You can convert decimal to hex with long division or a lookup table. Long division shows each quotient and remainder. A lookup table works best for frequent values.

Formula: $n = 16q + r$

Long Division Method

Divide the decimal number by 16. Keep each remainder, then divide the quotient again. Continue until the quotient is 0. Convert remainders 10 to 15 into A to F, then read upward.

Lookup Table Method

Find the decimal number in a conversion table and read its matching hex value. This saves time for 10 = A, 16 = 10, and 255 = FF.

Decimal to Hex conversion table

Note: Hex uses 0 to 9 and A to F. Each hex digit represents four binary bits, so 00 to FF covers byte values from 0 to 255. Leading zeros can keep fixed widths.

Decimal to Hex Conversion in Programming

Programmers often use hexadecimal to display binary data in a shorter form. Python and C both provide simple ways to convert decimal integers into hexadecimal.

Decimal to Hex in Python

Python provides the hex() function for decimal to hexadecimal conversion.

number = 45
result = hex(number)

print(result)

Output:

0x2d

If you want uppercase hex without the 0x prefix, use:

number = 45
result = format(number, "X")

print(result)

Output:

2D

Decimal to Hex in C

C can convert a decimal integer to hexadecimal with printf() and the %X format specifier.

#include <stdio.h>

int main() {
int number = 45;

printf("%X", number);

return 0;
}

Output:

2D

Use %x when you want lowercase hexadecimal, such as 2d.