Decimal to hexadecimal converter

What is the decimal number system?

The decimal number system, also called the base-10 system, is the most commonly used numbering system in daily life. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit in a number represents a power of ten, depending on its position.

For example, in the number 427, the digit 7 represents $7 \times 10^0$, the 2 represents $2 \times 10^1$, and the 4 represents $4 \times 10^2$. Adding all together, we get:
$427 = 4 \times 100 + 2 \times 10 + 7 \times 1$.

This positional value concept forms the basis of all number systems.

What is the hexadecimal number system?

The hexadecimal number system, or base-16 system, uses sixteen possible symbols for each digit: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.
Here, the letters represent the decimal numbers 10 through 15:

• A = 10
• B = 11
• C = 12
• D = 13
• E = 14
• F = 15

This system is compact and efficient. It is especially important in computing and digital electronics, where binary numbers (base 2) are used internally. A single hexadecimal digit corresponds exactly to four binary digits (bits), making conversions easy.

For example, the hexadecimal number 2F equals $2 \times 16^1 + F \times 16^0 = 2 \times 16 + 15 = 47$ in decimal form.

Formula

To convert a decimal number into a hexadecimal one, repeated division by 16 is used.
Each time, the remainder represents one hexadecimal digit, starting from the least significant position (rightmost digit).

Let a decimal number $N$ be given. Divide $N$ by 16 until the quotient becomes zero.
The relationship can be summarized as:

$$N = (r_k \times 16^k) + (r_{k-1} \times 16^{k-1}) + ... + (r_1 \times 16^1) + (r_0 \times 16^0)$$

Where:

• $r_i$ is the remainder obtained at each division step (converted to hexadecimal symbol if needed)
• The final hexadecimal number is read from bottom remainder to top remainder

Step-by-step example: Convert 256 (decimal) to hexadecimal

To understand the process more clearly, let’s follow each division step:

Now, starting from the bottom remainder and moving upward gives us:
100₁₆ (hexadecimal representation of 256).

So $256_{10} = 100_{16}$.

Example 2: Convert 43981 (decimal) to hexadecimal

Reversing the remainders: ABCD₁₆

Thus, $43981_{10} = ABCD_{16}$.

Quick conversion tips

1. Divide the decimal number by 16 repeatedly.
2. Record the remainder each time – convert values 10–15 into A–F.
3. Reverse the order of collected remainders to get the final hexadecimal value.
4. For very large numbers, using a calculator is much faster and avoids manual errors.

Applications of the hexadecimal system

1. Computing and programming: Hexadecimal numbers represent memory addresses and color codes.
   For example, the color code #FF0000 represents pure red.
   The three pairs (FF, 00, 00) show red, green, and blue intensity in hexadecimal.
2. Digital electronics: Used for data representation in binary systems; shortened hexadecimal form simplifies binary sequences.
3. Networking: MAC addresses and IPv6 addresses use hexadecimal notation for compactness.
4. Debugging systems: Software engineers use hex dumps to view binary data in readable form.

Frequently asked questions

How to convert 500 in decimal to hexadecimal manually?

Divide 500 repeatedly by 16:

Reading from bottom: 1F4₁₆.
$500_{10} = 1F4_{16}$.

How many hexadecimal digits are needed to represent a byte?

A byte equals 8 bits, and each hexadecimal digit equals 4 bits.
Therefore, $8 ÷ 4 = 2$ digits.
One byte is represented by exactly two hexadecimal characters.

How to check if a hexadecimal number is valid?

Verify that all characters belong to: 0–9 and A–F.
Any other character (like G or Z) is not valid in hexadecimal representation.

What is the largest hexadecimal number that fits in a single byte?

A byte = 8 bits = $2^8 - 1 = 255$ in decimal.
The hexadecimal equivalent of 255 is FF₁₆.

Why is hexadecimal preferred over binary in programming?

Binary numbers are long and hard to read. Hexadecimal condenses them, using 1 hex digit per 4 binary bits, making reading and debugging far more efficient. For instance, the binary string 11111111 becomes simple FF₁₆.