Decimal to Hex Conversion

Decimal to hex conversion is often used in computers and the digital world. While we use the decimal number system (base 10) in our daily life, computers often use the hexadecimal system (base 16) because it offers a more compact and human-friendly way to represent binary data. HTML/CSS colour codes, memory addresses on computers, and binary code debugging are some of the examples where decimal to hex conversion holds importance. Therefore, converting decimal numbers to hexadecimal is an important skill in programming, networking, and digital design. 

 In this article, we will learn what decimal and hexadecimal numbers are and why decimal to hex conversion is necessary, along with a step-by-step explanation of how to perform it.

Table of Contents

• Decimal Number System
• Hexadecimal Number System
• Basic Hexadecimal Digits
• Why Convert Decimal to Hex?
• Step-by-Step Guide to Decimal to Hex Conversion
• Example of Decimal to Hex Conversion
• Common Applications of Hexadecimal Numbers
• FAQs on Decimal to Hex Conversion

Decimal Number System

The decimal system is the standard number system used by us in our day-to-day life. It is defined as a standard number system that uses 0-9 digits to represent any number. It is a base 10 number system, meaning it uses ten digits from 0 to 9. Each digit’s position represents a power of 10. For example, the number 1345 means 1x1000+3x100+4x10+5=345

Hexadecimal Number System

Hexadecimal (or hex) is a base 16 number system; that is, it uses 16 digits from 0 to 9 for values zero to nine and A to F for values ten to fifteen. Each digit’s position represents a power of 16. For example, the hex number 1A3 means (1 * 162) + (10 * 161) + (3 * 16) = 256 + 160 + 3 = 419.

Basic Hexadecimal Digits

 

Why Convert Decimal to Hex?

The conversion of decimal to hex is a process of converting a number with base 10 to a number with base 16.

It is useful in the following ways:

• Compact representation: Hexadecimal numbers are shorter and easier to read than long binary strings.

• Used in programming: Many programming languages use hex to represent memory addresses or colour codes.

• Digital systems: Hex is a natural fit for binary data since 1 hex digit equals 4 binary bits.
  
  

Step-by-Step Guide to Decimal to Hex Conversion

Although you can find an online decimal-hexadecimal converter easily, it is always useful to learn how to learn the manual process of dec to hex. 

1. Divide the decimal number by 16.

2. Write down the remainder (this is the least significant digit in hex).

3. Divide the quotient again by 16.

4. Repeat until the quotient is zero.

The hex number is the remainders read in reverse order (from last remainder to first).

Example of Decimal to Hex Conversion

Let’s learn how to convert decimal 254 to hexadecimal:

254 ÷ 16 = 15 remainder 14 → remainder 14 = E

 15 ÷ 16 = 0 remainder 15 → remainder 15 = F

 Reading remainders from last to first: FE

 So, decimal 254 = hex FE

Common Applications of Hexadecimal Numbers 

Decimal to hexadecimal conversion is a fundamental concept in computing. It enables easier representation and understanding of binary data. By following the division and remainder method, anyone can convert decimal numbers into their hexadecimal equivalents. Learn more about the hexadecimal number system and hex to decimal conversion with Orchid.

 

FAQs on Decimal to Hex Conversion

1: What is decimal to hexadecimal conversion?

A: The process of converting a decimal number with base 10 to a hexadecimal number with base 16 is called decimal-to-hexadecimal conversion.

2: How to convert a decimal number into a hexadecimal number?

A: To convert any decimal number into a hexadecimal number, keep dividing the number by 16 until the quotient becomes zero. Combine and note down the reminders in reverse order to get the converted number. Never forget to replace the 11, 12, 13, 14, and 15 with A, B, C, D, E, and F, respectively. 

3: How do computers convert decimal to hex?

A: Computers usually work directly with binary and convert to hex for display purposes, often using built-in functions.