Decimal to Hex Converter: Concepts, Table and Solved Examples

Nam Generator

Tools

Decimal to Hex Converter

Decimal to Hex Converter

Size: 0 Bytes, 0 Characters
Size: 0 Bytes, 0 Characters

Nam Generator is your go-to resource for a variety of tools, including our efficient and easy-to-use Decimal to Hex Converter. This tool allows you to convert decimal (base 10) numbers into hexadecimal (base 16) numbers with ease. In this article, we’ll explore the importance of converting decimals to hex, how the conversion works, and why it matters in computing. In digital computing, conversions between number systems are critical. One of the most commonly used conversions is from decimal to hexadecimal.

Read More: Decimal to Octal Converter

What is a Decimal Number?

Decimal numbers are part of the base-10 numbering system, which is the most widely used system in our daily lives. It includes the digits 0 through 9. For example, the number “245” is a decimal number that consists of the digits 2, 4, and 5.

Base-10 System

  • Uses digits 0–9
  • Powers of 10: 100,101,102,…10^0, 10^1, 10^2, \dots100,101,102,…

What is a Hexadecimal Number?

Hexadecimal, or hex, is a base-16 numbering system used mainly in computing and digital systems. It uses sixteen symbols: the digits 0-9 and the letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15). Hexadecimal numbers are often used because they represent binary data in a more human-readable format.

Base-16 System

  • Uses digits 0-9 and letters A-F
  • Powers of 16: 160,161,162,…16^0, 16^1, 16^2, \dots160,161,162,…

Why Convert Decimal to Hexadecimal?

Hexadecimal numbers are commonly used in programming, computer memory addressing, and color coding in web design. Some reasons to convert decimal to hex include:

  • Efficient Representation: Hexadecimal can represent large binary numbers in a shorter format.
  • Memory Addressing: Hex is used in computer memory to address locations in a more compact form.
  • Color Codes: Hexadecimal codes are used to represent colors in web design (e.g., #FF5733).

How to Convert Decimal to Hex Manually

While using the Nam Generator converter is the easiest way to get the result instantly, it’s good to know how to convert decimal to hex manually. Here’s the step-by-step process:

Step 1: Divide by 16

Divide the decimal number by 16 and note the quotient and remainder.

Step 2: Remainders as Hex Digits

The remainder becomes the hex digit. If it’s 10 or higher, use letters A-F.

Step 3: Continue the Process

Keep dividing the quotient by 16 until the quotient is zero.

Step 4: Read the Hex

The hex number is read from the last remainder to the first.

Example: Convert 245 to Hex

  1. 245÷16=15245 \div 16 = 15245÷16=15 (remainder 5)
  2. 15÷16=015 \div 16 = 015÷16=0 (remainder 15, which is F)

So, 245 in decimal is F5 in hex.

Using the Decimal to Hex Converter on Nam Generator

Our Decimal to Hex Converter is designed for simplicity. All you need to do is:

  1. Enter the decimal number in the input box.
  2. Click the “Convert” button.
  3. Instantly get the hexadecimal equivalent.

No complex calculations, no hassle — just fast and accurate conversions!

Decimal to Hexadecimal Formula

Converting a decimal number to its hexadecimal equivalent involves dividing the decimal number by 16 and recording the remainder. The steps are repeated until the quotient becomes zero. The remainders are then read in reverse order to get the hexadecimal number.

Formula:

For any decimal number NNN, the conversion can be done using:N=∑i=0kdi×16iN = \sum_{i=0}^{k} d_i \times 16^iN=i=0∑k​di​×16i

Where:

  • did_idi​ is the digit at position iii in the hexadecimal representation.
  • kkk is the number of digits in the resulting hexadecimal number.

Steps:

  1. Divide the decimal number by 16.
  2. Write down the remainder (this gives the hex digit).
  3. Divide the quotient again by 16.
  4. Repeat the process until the quotient is 0.
  5. Read the remainders in reverse to form the hexadecimal value.
Decimal to Hexadecimal Table

To assist with conversion, here is a reference table of decimal numbers and their corresponding hexadecimal values:

DecimalHexadecimal
00
11
22
33
44
55
66
77
88
99
10A
11B
12C
13D
14E
15F
Decimal to Hexadecimal Converter with Steps

Let’s walk through the process of converting a decimal number to hexadecimal with steps.

Example:

Convert the decimal number 345 to hexadecimal:

  1. 345 ÷ 16 = 21 with a remainder of 9 (this is the least significant digit, LSB).
  2. 21 ÷ 16 = 1 with a remainder of 5.
  3. 1 ÷ 16 = 0 with a remainder of 1 (this is the most significant digit, MSB).

Therefore, the hexadecimal equivalent of 345 is 159.

Shortcut:

For faster conversion, you can use online tools that automatically provide a step-by-step solution by inputting the decimal number and receiving the hexadecimal equivalent.

Decimal to Hexadecimal Conversion Examples

Here are some common decimal to hex converter examples:

  1. Decimal 255 to Hexadecimal
    Steps:
    255÷16=15255 \div 16 = 15255÷16=15, remainder 15 (F)
    Hexadecimal result: FF
  2. Decimal 512 to Hexadecimal
    Steps:
    512÷16=32512 \div 16 = 32512÷16=32, remainder 0
    32÷16=232 \div 16 = 232÷16=2, remainder 0
    Hexadecimal result: 200
  3. Decimal 1024 to Hexadecimal
    Steps:
    1024÷16=641024 \div 16 = 641024÷16=64, remainder 0
    64÷16=464 \div 16 = 464÷16=4, remainder 0
    Hexadecimal result: 400

Hexadecimal to Decimal to Binary Conversion

Understanding how to switch between hexadecimal, decimal, and binary systems is important in computing.

Hexadecimal to Decimal:

To convert from hexadecimal to decimal, multiply each hex digit by the power of 16 corresponding to its position.

Example: Convert A5 to decimal:(10×161)+(5×160)=165(10 \times 16^1) + (5 \times 16^0) = 165(10×161)+(5×160)=165

Decimal equivalent: 165

Decimal to Binary:

To convert decimal to binary, repeatedly divide by 2 and record the remainders. Read them in reverse.

Example: Convert 165 to binary:165÷2=82 R1, 82÷2=41 R0, 41÷2=20 R1, 20÷2=10 R0, 10÷2=5 R0, 5÷2=2 R1, 2÷2=1 R0, 1÷2=0 R1165 ÷ 2 = 82 \text{ R}1,\ 82 ÷ 2 = 41 \text{ R}0,\ 41 ÷ 2 = 20 \text{ R}1,\ 20 ÷ 2 = 10 \text{ R}0,\ 10 ÷ 2 = 5 \text{ R}0,\ 5 ÷ 2 = 2 \text{ R}1,\ 2 ÷ 2 = 1 \text{ R}0,\ 1 ÷ 2 = 0 \text{ R}1165÷2=82 R1, 82÷2=41 R0, 41÷2=20 R1, 20÷2=10 R0, 10÷2=5 R0, 5÷2=2 R1, 2÷2=1 R0, 1÷2=0 R1

Binary result: 10100101

Decimal to Octal Conversion

Decimal to octal conversion is similar to decimal-to-hex, except that you divide by 8 instead of 16.

Example:

Convert decimal 345 to octal:

  1. 345 ÷ 8 = 43 remainder 1
  2. 43 ÷ 8 = 5 remainder 3
  3. 5 ÷ 8 = 0 remainder 5

Therefore, the octal equivalent of 345 is 531.

16 in Hexadecimal

The number 16 in decimal can be easily converted to hexadecimal using the standard method of dividing by 16.

  • 16÷16=116 \div 16 = 116÷16=1 with a remainder of 0.

Therefore, 16 in hexadecimal is written as 10.

Conclusion:

The process of converting decimal to hexadecimal is straightforward with the proper understanding of the steps involved. From manual calculations using division and remainders to using tables for quick reference or online tools for instant conversion, the decimal to hexadecimal system is integral to modern computing.

Read More: Decimal to Hex Converter

FAQs:

What is a Decimal to Hex Converter?
A tool or formula used to convert a decimal number into its hexadecimal equivalent.

How do you convert decimal to hex manually?
Divide the decimal by 16, record the remainder, repeat for the quotient, and read the remainders in reverse.

What is hexadecimal?
A base-16 number system used in computing, using digits 0-9 and letters A-F.

Why is hexadecimal used in computing?
Hexadecimal efficiently represents large binary numbers and is easier to read for humans.

What is the hex value of 255 in decimal?
The hexadecimal value of 255 is FF.

How is hex different from decimal?
Hexadecimal is base-16, while decimal is base-10.

Can a calculator convert decimal to hex?
Yes, many scientific calculators have built-in functionality for converting decimal to hex.

What is the largest single-digit number in hex?
The largest single-digit hex number is F, representing decimal 15.

What is the hexadecimal equivalent of 16?
The hexadecimal equivalent of 16 is 10.

Is there an easy way to convert decimal to hex?
Yes, you can use online decimal to hex converters for quick results.

What is the formula for converting decimal to hex?
Divide the decimal by 16, and continue until the quotient is 0, reading remainders in reverse.

How is hex used in programming?
Hexadecimal is often used to represent memory addresses, colors in web design, and more.

What is the smallest hex digit?
The smallest hex digit is 0, just like in decimal.

What is a hexadecimal table?
A reference chart that shows decimal numbers and their corresponding hexadecimal values.

Can hex numbers include letters?
Yes, hexadecimal uses A-F to represent values 10-15.

How do you convert hexadecimal back to decimal?
Multiply each hex digit by the power of 16 according to its position.

What is the hexadecimal representation of 1000?
The hexadecimal value of 1000 is 3E8.

Is hex conversion common in everyday use?
It’s common in computing, especially in fields like programming and digital electronics.

What is the hexadecimal value for 1024?
The hex value for 1024 is 400.

How can I convert large decimal numbers to hex?
For large numbers, it’s recommended to use a calculator or an online converter tool.

Leave a Comment

At Namgenerator.com, we’re passionate about creativity, innovation, and helping businesses find their perfect identity. Our AI-powered tools—whether it’s business name generation or keyword research—empower you to make informed decisions. Unlock the potential of your brand with Namgenerator.com!

Social Media