Binary to Hexadecimal Calculator

Convert between binary (base-2) and hexadecimal (base-16) number systems instantly. This calculator is essential for programmers, computer science students, and anyone working with digital systems.

Understanding Number Systems

Binary (Base-2)

• Uses only two digits: 0 and 1
• Each position represents a power of 2
• Common in digital electronics and computing
• Example: 1010 (binary) = 10 (decimal)

Hexadecimal (Base-16)

• Uses sixteen digits: 0-9 and A-F
• A=10, B=11, C=12, D=13, E=14, F=15
• Compact representation of binary data
• Example: A5 (hex) = 165 (decimal)

Binary-Hex Conversion Table

Hex	Binary	Hex	Binary
0	0000	8	1000
1	0001	9	1001
2	0010	A	1010
3	0011	B	1011
4	0100	C	1100
5	0101	D	1101
6	0110	E	1110
7	0111	F	1111

How to Convert Binary to Hexadecimal

1. Group Binary Digits
   • Start from the right
   • Create groups of 4 bits
   • Add leading zeros if needed
2. Convert Each Group
   • Use the conversion table
   • Replace each 4-bit group with its hex digit
3. Combine Results
   • Write hex digits from left to right
   • Remove leading zeros

Example: 1010 1111 → AF (hex)

How to Convert Hexadecimal to Binary

1. Convert Each Hex Digit
   • Use the conversion table
   • Replace each hex digit with 4 bits
2. Combine Results
   • Write all bits together
   • Remove leading zeros if desired

Example: C5 → 1100 0101 (binary)

Common Applications

1. Computer Programming

   • Memory addresses
   • Color codes (e.g., #FF0000 for red)
   • Binary file representations

2. Digital Electronics

   • Microcontroller programming
   • Digital signal processing
   • Hardware debugging

3. Network Engineering

   • MAC addresses
   • IPv6 addresses
   • Network masks

Tips for Accurate Conversion

1. Binary Numbers
   • Verify only 0s and 1s are used
   • Group into sets of 4 bits
   • Add leading zeros when needed
2. Hexadecimal Numbers
   • Use only valid hex digits (0-9, A-F)
   • Case doesn’t matter (a-f or A-F)
   • Remove leading zeros

Technical Notes

• Maximum input length: 16 bits
• Supports both uppercase and lowercase hex
• Automatic validation of input format
• Real-time conversion updates

Frequently Asked Questions

Q: Why use hexadecimal instead of decimal? A: Hexadecimal provides a more compact representation of binary data, where each hex digit represents exactly 4 bits.

Q: Are leading zeros important? A: Leading zeros don’t change the value but can be important for formatting or when a specific number of digits is required.

Q: Is hex case-sensitive? A: No, both uppercase (A-F) and lowercase (a-f) are valid and represent the same values.