Decimal to Hexadecimal Converter

What is Decimal to Hexadecimal Conversion?

Decimal to hexadecimal conversion is the process of transforming a number from base 10 (decimal) to base 16 (hexadecimal). This conversion is widely used in computer science and digital systems.

Formula and Representation

The general formula for converting a decimal number to hexadecimal is:

\[D_{10} = (d_n \times 16^n) + (d_{n-1} \times 16^{n-1}) + ... + (d_1 \times 16^1) + (d_0 \times 16^0)\]

Where:

• \(D_{10}\) is the decimal number
• \(d_n, d_{n-1}, ..., d_1, d_0\) are hexadecimal digits (0-9, A-F)
• \(n\) is the position of the digit (starting from 0 for the rightmost digit)

Calculation Steps

1. Divide the decimal number by 16.
2. Keep track of the quotient and the remainder.
3. Repeat steps 1 and 2 using the quotient from the previous division until the quotient becomes 0.
4. The remainders in reverse order form the hexadecimal number.

Example

Let's convert the decimal number 2748 to hexadecimal:

\[2748 \div 16 = 171 \text{ remainder } 12 \text{ (C)}\] \[171 \div 16 = 10 \text{ remainder } 11 \text{ (B)}\] \[10 \div 16 = 0 \text{ remainder } 10 \text{ (A)}\]

Reading the remainders from bottom to top, we get:

\[2748_{10} = ABC_{16}\]

Visual Representation

Here's a visual representation of the conversion process:

  2748 | 16
  ---- -----
   171   12 (C)
    10   11 (B)
     0   10 (A)

This diagram shows how we repeatedly divide by 16 and collect the remainders to form the hexadecimal number ABC.