Decimal to Hexadecimal Converter with Steps

Decimal to Hexadecimal Conversion

Converting a decimal number to hexadecimal is a useful technique in computing and digital electronics, especially when working with memory addresses, colors in web design, and low-level programming. The hexadecimal system is base-16, using digits 0–9 and letters A–F to represent values.

What is Decimal?

Decimal is the standard base-10 number system we use in everyday life. It includes digits from 0 to 9. Each digit’s position represents a power of 10. For example, 245 in decimal means: (2×10²) + (4×10¹) + (5×10⁰).

What is Hexadecimal?

The hexadecimal (or hex) system is base-16. It includes digits from 0 to 9 and letters A to F, where A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15. It is widely used in programming, color codes (e.g., #FF5733), and memory representation in computers.

How to Convert Decimal to Hexadecimal (Integer Part)

To convert a whole number (integer) from decimal to hexadecimal:

1. Divide the decimal number by 16.
2. Record the remainder (convert 10-15 to A-F).
3. Continue dividing the quotient by 16 until you reach 0.
4. The hexadecimal number is the remainders read from bottom to top.

Example: Convert 345 to Hexadecimal

• 345 \(\div\) 16 = 21 remainder 9 \(\rightarrow\) 9
• 21 \(\div\) 16 = 1 remainder 5 \(\rightarrow\) 5
• 1 \(\div\) 16 = 0 remainder 1 \(\rightarrow\) 1

Reading from bottom to top, 345 in decimal = 159 in hexadecimal.

How to Convert Decimal Fractions to Hexadecimal

To convert a fractional decimal (e.g., 0.625) to hexadecimal:

1. Multiply the fractional part by 16.
2. The integer part of the result becomes the next hex digit.
3. Repeat the process with the new fractional part.
4. Stop after a few digits or when the fraction becomes 0.

Example: Convert 0.625 to Hexadecimal

• \(0.625 \times 16 = 10.0 \rightarrow \) Integer part: 10 = A
• Fractional part is now 0, so we stop.

So, 0.625 in decimal = 0.A in hexadecimal.

Example: Convert 0.3 to Hexadecimal

• \(0.3 \times 16 = 4.8 \rightarrow 4 \)
• \(0.8 \times 16 = 12.8 \rightarrow 12 \) = C
• \(0.8 \times 16 = 12.8 \rightarrow \) continues repeating...

So, 0.3 in decimal \(\approx\) 0.4CCCC... (repeating) in hexadecimal.

Combining Integer and Fractional Parts

To convert a decimal number with both integer and fraction (e.g., 345.625):

• Convert the integer part (345 \(\rightarrow\) 159)
• Convert the fractional part (0.625 \(\rightarrow\) A)
• Final hexadecimal: 159.A

Why Convert Decimal to Hexadecimal?

• Hex numbers are shorter and easier to read than binary.
• Used in computer memory addresses and debugging.
• Essential in web development for colors and CSS.

Use Our Decimal to Hexadecimal Calculator

Use our free Decimal to Hexadecimal Calculator above to instantly convert any number-integer or fractional-and view detailed steps showing how it's done.