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Decimal to Hex Converter



Converting a Decimal Number to Hexadecimal

Hexadecimal (or simply hex) is a base-16 number system that uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F (or a-f) to represent values ten to fifteen. Hexadecimal numbers are commonly used in computing and digital systems because they can represent binary values more compactly.

Each hex digit represents four binary digits (bits), which makes it easier to read and interpret large binary numbers. This system is particularly useful in programming, memory addressing, and other applications that require a concise representation of binary data.

To convert a decimal number (base 10) to hexadecimal (base 16), we repeatedly divide the number by 16, recording the remainder at each step. The hexadecimal equivalent is obtained by reading the remainders in reverse order, starting from the last division.

Examples

Let’s explore some examples to understand how to convert decimal numbers to their hexadecimal equivalents.

1. Convert the decimal number 285 to hexadecimal.

Answer

First, we identify the given number:

Given:

  • Decimal: 285

Next, we divide the number by 16, recording the quotient and remainder at each step:

Steps:

  • 285 ÷ 16 = 17, remainder = 13 (which is D in hexadecimal)
  • 17 ÷ 16 = 1, remainder = 1
  • 1 ÷ 16 = 0, remainder = 1

We then read the remainders from bottom to top:

Hexadecimal Equivalent:

11D

Result:

∴ The hexadecimal equivalent of the decimal number 285 is 11D.

2. Convert the decimal number 1024 to hexadecimal.

Answer

We start by identifying the number:

Given:

  • Decimal: 1024

Next, we divide the number by 16, recording the quotient and remainder at each step:

Steps:

  • 1024 ÷ 16 = 64, remainder = 0
  • 64 ÷ 16 = 4, remainder = 0
  • 4 ÷ 16 = 0, remainder = 4

We then read the remainders from bottom to top:

Hexadecimal Equivalent:

400

Result:

∴ The hexadecimal equivalent of the decimal number 1024 is 400.

3. Determine the hexadecimal equivalent of the decimal number 255.

Answer

First, we identify the given number:

Given:

  • Decimal: 255

Next, we divide the number by 16, recording the quotient and remainder at each step:

Steps:

  • 255 ÷ 16 = 15, remainder = 15 (which is F in hexadecimal)
  • 15 ÷ 16 = 0, remainder = 15 (which is F in hexadecimal)

We then read the remainders from bottom to top:

Hexadecimal Equivalent:

FF

Result:

∴ The hexadecimal equivalent of the decimal number 255 is FF.

4. Convert the decimal number 4096 to hexadecimal.

Answer

We start by identifying the number:

Given:

  • Decimal: 4096

Next, we divide the number by 16, recording the quotient and remainder at each step:

Steps:

  • 4096 ÷ 16 = 256, remainder = 0
  • 256 ÷ 16 = 16, remainder = 0
  • 16 ÷ 16 = 1, remainder = 0
  • 1 ÷ 16 = 0, remainder = 1

We then read the remainders from bottom to top:

Hexadecimal Equivalent:

1000

Result:

∴ The hexadecimal equivalent of the decimal number 4096 is 1000.