Decimal to Hex Converter: Convert Decimal to Hexadecimal
A decimal to hexadecimal converter transforms decimal numbers (base-10 numbers using digits 0-9) into hexadecimal numbers (base-16 numbers using digits 0-9 and letters A-F representing values 0-15) through repeated division by 16, tracking remainders that are then read in reverse order to obtain the hexadecimal representation essential for computer programming, web development, color coding, memory addressing, and digital system design. This conversion process uses the division-remainder method where the decimal number is repeatedly divided by 16, recording each remainder (0-9 or A-F), then reading these remainders from bottom to top to form the hex equivalent, enabling translation from human-readable decimal format to compact hexadecimal notation used in programming languages, web design (color codes), assembly language, debugging, memory dumps, and any application requiring efficient representation of binary data in a human-readable compact format.
🔢 Decimal to Hex Converter
Enter a decimal number to convert to hexadecimal
Maximum value: 2,147,483,647
Understanding Decimal to Hex Conversion
Decimal is the base-10 number system we use in everyday life, consisting of ten digits (0-9). Hexadecimal is a base-16 number system using sixteen symbols: digits 0-9 and letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15). Hex is extensively used in computing because it provides a compact way to represent binary data—each hex digit represents exactly four binary bits.
Decimal to Hex Formula
Division-Remainder Method:
Repeatedly divide the decimal number by 16
Record the remainder at each step (0-9 or A-F)
Read remainders from bottom to top
Mathematical Expression:
\[ N_{10} = d_n \times 16^n + d_{n-1} \times 16^{n-1} + \cdots + d_1 \times 16^1 + d_0 \times 16^0 \]
Where \( d_i \) are hex digits (0-F) at each position
Step-by-Step Conversion Method
Division-Remainder Algorithm
- Divide the decimal number by 16
- Record the remainder (0-9 directly, 10-15 as A-F)
- Divide the quotient by 16 again
- Repeat until quotient becomes 0
- Read remainders from bottom to top for hex result
- Convert remainders: 10→A, 11→B, 12→C, 13→D, 14→E, 15→F
Detailed Conversion Examples
Example 1: Convert Decimal 47 to Hex
Problem: Convert decimal 47 to hexadecimal
Step-by-step division:
Division Quotient Remainder Hex
47 ÷ 16 = 2 15 F ← LSB (rightmost)
2 ÷ 16 = 0 2 2 ← MSB (leftmost)
Read remainders bottom to top: 2F
Answer: 47₁₀ = 2F₁₆
Verification: (2×16) + (15×1) = 32 + 15 = 47 ✓
Example 2: Convert Decimal 255 to Hex
Problem: Convert decimal 255 to hexadecimal
Division process:
255 ÷ 16 = 15 remainder 15 (F)
15 ÷ 16 = 0 remainder 15 (F)
Reading bottom to top: FF
Answer: 255₁₀ = FF₁₆
Note: FF is the maximum value for one byte (8 bits)
Common use: RGB color values (0-255 per channel)
Example 3: Convert Decimal 1000 to Hex
Problem: Convert decimal 1000 to hexadecimal
Division steps:
1000 ÷ 16 = 62 R 8 → 8
62 ÷ 16 = 3 R 14 → E
3 ÷ 16 = 0 R 3 → 3
Reading bottom to top: 3E8
Answer: 1000₁₀ = 3E8₁₆
Verification: (3×256) + (14×16) + (8×1) = 768 + 224 + 8 = 1000 ✓
Decimal to Hex Conversion Table
| Decimal | Hexadecimal | Binary |
|---|---|---|
| 0 | 0 | 0000 |
| 1-9 | 1-9 | 0001-1001 |
| 10 | A | 1010 |
| 11 | B | 1011 |
| 12 | C | 1100 |
| 13 | D | 1101 |
| 14 | E | 1110 |
| 15 | F | 1111 |
| 16 | 10 | 10000 |
| 32 | 20 | 100000 |
| 100 | 64 | 1100100 |
| 255 | FF | 11111111 |
| 256 | 100 | 100000000 |
| 4096 | 1000 | - |
Remainder to Hex Digit Conversion
| Remainder (Decimal) | Hex Digit | Use in Conversion |
|---|---|---|
| 0-9 | 0-9 | Use directly (no conversion) |
| 10 | A | Convert to letter A |
| 11 | B | Convert to letter B |
| 12 | odede>C | Convert to letter C |
| 13 | D | Convert to letter D |
| 14 | E | Convert to letter E |
| 15 | F | Convert to letter F |
Real-World Applications
Web Development
- Color codes: RGB values in hex (#FF5733)
- CSS styling: Colors, opacity values
- URL encoding: Special character representation
- Image formats: Pixel data in hex
Programming
- Memory addresses: Pointer values in hex (0x7FFF)
- Character codes: ASCII, Unicode values
- Bit manipulation: Flags, masks in hex
- Debugging: Memory dumps, register values
- Cryptography: Hash values, keys
Digital Electronics
- MAC addresses: Network hardware IDs
- IPv6 addresses: Network addressing
- Firmware: Embedded system programming
- Data encoding: Compact binary representation
RGB Color Conversion Example
Convert RGB(255, 87, 51) to hex color code:
Red channel (255):
255 ÷ 16 = 15 R 15 → FF
Green channel (87):
87 ÷ 16 = 5 R 7 → 57
Blue channel (51):
51 ÷ 16 = 3 R 3 → 33
Result: #FF5733
CSS: color: #FF5733;
Quick Conversion Tips
Mental Math Shortcuts:
- Divide by 16: Quotient becomes next digit
- Remainders 0-9: Use as-is in hex
- Remainders 10-15: Convert to A-F
- Powers of 16: 16=10₁₆, 256=100₁₆, 4096=1000₁₆
- Multiples of 16: End in 0 in hex (32=20, 48=30)
- One less than power: All F's (255=FF, 4095=FFF)
Common Mistakes to Avoid
⚠️ Conversion Errors
- Reading remainders wrong direction: Must read bottom to top
- Forgetting to convert 10-15: Must use A-F, not two digits
- Using lowercase vs uppercase: Both valid (FF = ff) but be consistent
- Stopping too early: Continue until quotient is 0
- Arithmetic mistakes: Double-check division steps
- Missing 0x prefix: Convention in programming (0xFF)
- Confusing with decimal: 10₁₆ = 16₁₀, not 10₁₀
Hex Digit Memory Aid
Remember A-F Values:
A = 10 (A is first letter after digits)
B = 11 (B comes after A)
C = 12 (Continue the pattern)
D = 13 (D is fourth letter)
E = 14 (E is fifth letter)
F = 15 (F is sixth and final hex letter)
Powers of 16 Reference
| Power | Decimal Value | Hex Representation |
|---|---|---|
| 16⁰ | 1 | 1 |
| 16¹ | 16 | 10 |
| 16² | 256 | 100 |
| 16³ | 4,096 | 1000 |
| 16⁴ | 65,536 | 10000 |
Frequently Asked Questions
How do you convert decimal to hex by hand?
Use division-remainder method: repeatedly divide decimal by 16, recording remainders. Convert remainders 10-15 to A-F. Continue until quotient is 0. Read remainders bottom to top. Example: 47÷16=2 R15(F), 2÷16=0 R2. Reading up: 2F. Always convert 10→A, 11→B, 12→C, 13→D, 14→E, 15→F. Verify by converting back to decimal: (2×16)+15=47. Practice makes this process quick and intuitive.
Why is hexadecimal used in programming?
Hex is compact representation of binary data. Each hex digit represents exactly 4 binary bits (nibble). One byte (8 bits) = 2 hex digits (00-FF). More readable than long binary strings. Example: binary 11111111 = hex FF = decimal 255. Two characters represent full byte. Used for memory addresses, color codes, debugging, bit patterns. Direct mapping to binary makes conversions easy. Standard in assembly language, systems programming, web development.
What is the hex equivalent of decimal 100?
Decimal 100 equals hexadecimal 64. Calculation: 100÷16=6 R4, 6÷16=0 R6. Reading up: 64. Verification: (6×16)+4=96+4=100. Common value in programming. Note: 64₁₆ ≠ 64₁₀. Always specify base to avoid confusion. In code: 0x64 = 100 decimal. Used in ASCII codes, percentages, RGB colors. Easy to remember pattern: 100 decimal = 64 hex because 6×16=96, plus 4=100.
How do you convert large decimal numbers to hex?
Same division method works for any size. Keep dividing by 16 until quotient is 0. For very large numbers, use calculator or programming tools. Example: 1,000,000÷16=62,500 R0, continue dividing. Result: F4240₁₆. Each division reduces number by factor of 16. More divisions = more hex digits. 2 hex digits = up to 255, 4 hex digits = up to 65,535, 6 hex digits = up to 16,777,215. Online converters instant for large values.
Can decimal fractions be converted to hex?
Yes! Fractional part uses multiplication method instead of division. Multiply fraction by 16, take integer part as hex digit, repeat with new fraction. Example: 0.5₁₀. 0.5×16=8.0, digit=8. Result: 0.8₁₆. Another: 0.75₁₀. 0.75×16=12.0, digit=C. Result: 0.C₁₆. Not all decimal fractions have exact hex equivalents (repeating hex). Used in floating-point representation, graphics programming. Whole and fractional parts converted separately, combined with hex point.
What does the 0x prefix mean?
0x indicates hexadecimal in programming languages (C, C++, Java, Python, JavaScript). Example: 0xFF means hex FF (decimal 255). Prevents confusion with decimal values or variable names. Without prefix, FF looks like variable. Convention standardizes code readability. Alternative: #FF in CSS colors, h suffix in assembly (FFh), $ in some systems. Always use 0x in code unless language requires different notation. Helps compilers/interpreters recognize number base.
Key Takeaways
Converting decimal to hexadecimal is essential for computer programming, web development, and digital system design. The division-remainder method provides a systematic approach to transform decimal numbers into compact hexadecimal notation, crucial for understanding memory addresses, color codes, and binary data representation.
Essential principles to remember:
- Hex uses base-16: digits 0-9 and letters A-F
- Division-remainder method: divide by 16, record remainders
- Convert remainders: 10→A, 11→B, 12→C, 13→D, 14→E, 15→F
- Read remainders bottom to top for hex result
- Each hex digit = 4 binary bits exactly
- Two hex digits = one byte (00-FF = 0-255)
- 0x prefix indicates hex in programming
- Powers of 16: 1, 16, 256, 4096, 65536
- Verify by converting back to decimal
- Practice with color codes for real-world application
Getting Started: Use the interactive converter at the top of this page to convert any decimal number to hexadecimal instantly. Enter your decimal value, click convert, and receive the hex result with complete step-by-step breakdown showing the division process, remainder conversion (including A-F letters), and verification calculation. Perfect for web development, programming, color code creation, or learning hexadecimal number systems.
