Decimal to Hexadecimal Converter
Convert decimal numbers to hexadecimal numbers easily and accurately.
Enter Your Number
Table of Contents
Comprehensive Guide to Decimal and Hexadecimal Systems
Understanding Number Systems
Number systems are the foundation of how we represent quantities. Different number systems use different bases (or radixes) that determine how many unique digits are used before we need to add a new position.
The Decimal Number System (Base-10)
The decimal system is our everyday counting system that uses 10 distinct digits (0-9). This system likely evolved because humans have 10 fingers, making it intuitive for counting.
Key characteristics of the decimal system:
- Uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9
- Position values increase by powers of 10 (ones, tens, hundreds, thousands...)
- Each position represents 10 times the value of the position to its right
The Hexadecimal Number System (Base-16)
The hexadecimal (or "hex") system uses 16 distinct symbols, requiring the addition of letters A through F to represent values 10 through 15.
Key characteristics of the hexadecimal system:
- Uses 16 symbols: 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15)
- Position values increase by powers of 16
- Each position represents 16 times the value of the position to its right
- Often prefixed with "0x" in programming contexts (e.g., 0x1A3F)
Why Hexadecimal is Important in Computing
Hexadecimal notation is extensively used in computing for several important reasons:
- Compact Representation: Hex provides a more compact way to represent binary data. One hex digit represents exactly 4 bits (a nibble), making conversion between hex and binary straightforward.
- Memory Addresses: Computer memory addresses are often displayed in hexadecimal format (e.g., 0x7FFFD4).
- Color Codes: Web colors are typically expressed as hex triplets (e.g., #FF5733 for a shade of orange).
- Debugging: Programmers often use hex when debugging because it's easier to read than binary but still directly maps to the binary values that computers use.
- Assembly Language: Machine code instructions are often represented in hexadecimal.
Relationship Between Binary and Hexadecimal
One of the most powerful aspects of hexadecimal is its direct relationship with binary:
| Hexadecimal | Binary | Decimal |
|---|---|---|
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 9 | 1001 | 9 |
| A | 1010 | 10 |
| F | 1111 | 15 |
Each hexadecimal digit maps to exactly four binary digits, making conversion between the two systems extremely efficient. For example, the hexadecimal number 1A3F translates directly to binary as 0001 1010 0011 1111.
Mathematical Foundation of Decimal to Hexadecimal Conversion
The conversion from decimal to hexadecimal is based on a fundamental mathematical principle: the positional notation system.
For a hexadecimal number with n digits dn-1...d1d0, its decimal value is:
For example, the hexadecimal number 2AF is calculated in decimal as:
= (2 × 256) + (10 × 16) + (15 × 1)
= 512 + 160 + 15
= 687
Applications of Hexadecimal Numbers
Web Development
Hex color codes (e.g., #FF5733) specify RGB values for web elements
Computer Hardware
Memory addresses and hardware values are often expressed in hex
Digital Security
Encryption keys and hashes are commonly represented in hex notation
Low-level Programming
Debugging, memory inspection, and bitwise operations often use hex
How to Convert Decimal to Hexadecimal
To convert decimal to hexadecimal, we repeatedly divide the decimal number by 16 and use the remainders to form the hexadecimal number.
Steps to Convert:
-
1Divide the decimal number by 16
-
2Write down the remainder (0-9 or A-F)
-
3Repeat with the quotient until it becomes 0
-
4Read the remainders from bottom to top
26 ÷ 16 = 1 remainder 10 (A)
1 ÷ 16 = 0 remainder 1
Result: 1A
Decimal to Hexadecimal Conversion Table:
0 = 0
1 = 1
2 = 2
3 = 3
4 = 4
5 = 5
6 = 6
7 = 7
8 = 8
9 = 9
10 = A
11 = B
12 = C
13 = D
14 = E
15 = F
Common Examples
Example 1 Basic Numbers
0 = 0
1 = 1
2 = 2
Example 2 Common Values
10 = A
16 = 10
32 = 20
Example 3 Mixed Numbers
26 = 1A
42 = 2A
255 = FF
Example 4 Larger Numbers
256 = 100
512 = 200
1024 = 400