Binary Hex Converter
Number system & bitwise operations
Enter Number
Common Values
Bit Distribution
Base Comparison
Bitwise Operations
Perform bitwise operations on two numbers
Bitwise Operations Explained
AND (&)
Returns 1 if both bits are 1, otherwise 0. Used for masking bits
OR (|)
Returns 1 if at least one bit is 1. Used for setting bits
XOR (^)
Returns 1 if bits are different. Used for toggling bits
NOT (~)
Inverts all bits (0→1, 1→0). Also called complement
Left Shift (<<)
Shifts bits left by n positions. Multiplies by 2^n
Right Shift (>>)
Shifts bits right by n positions. Divides by 2^n
ASCII Character Table
| Decimal | Hex | Binary | Character | Description |
|---|
Understanding Number Systems
What are Number Bases?
A number base (or radix) defines how many unique digits are used to represent numbers. The most common bases in computing are:
- Binary (Base 2): Uses digits 0 and 1. Fundamental to all digital computers
- Octal (Base 8): Uses digits 0-7. Was popular in early computing
- Decimal (Base 10): Uses digits 0-9. Standard human numbering system
- Hexadecimal (Base 16): Uses digits 0-9 and A-F. Compact representation of binary
Conversion Methods
Common conversion techniques:
- Binary to Decimal: Sum of (bit × 2^position). Example: 1010 = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 10
- Decimal to Binary: Repeated division by 2, collect remainders
- Binary to Hex: Group binary into 4-bit groups, convert each group
- Hex to Binary: Convert each hex digit to 4-bit binary
- Binary to Octal: Group binary into 3-bit groups, convert each group
Why Hexadecimal?
Hexadecimal is widely used in computing because:
- Compact: Each hex digit represents 4 binary bits
- Readable: Easier for humans to read than long binary strings
- Aligned: 2 hex digits = 1 byte (8 bits)
- Colors: Web colors use hex (#RRGGBB)
- Memory addresses: Typically displayed in hex
Quick Conversion Tricks
- Binary ↔ Hex: Group by 4 bits. 1111 = F, 1010 = A, 0101 = 5
- Binary ↔ Octal: Group by 3 bits. 111 = 7, 110 = 6, 101 = 5
- Powers of 2: 2⁰=1, 2¹=2, 2²=4, 2³=8, 2⁴=16, 2⁸=256
- Byte values: 0-255 (8 bits), 0-65535 (16 bits)
Practical Applications
- Programming: Bitwise operations, flags, masks
- Networking: IP addresses, MAC addresses, subnet masks
- Web Development: Color codes (#RRGGBB)
- Hardware: Memory addresses, register values
- Cryptography: Encryption algorithms, hash functions
Tips & Tricks
Hex Digits
0-9 = 0-9, A=10, B=11, C=12, D=13, E=14, F=15
Binary Groups
Group binary by 4 for hex, by 3 for octal. Makes conversion easy
Prefix Notation
0b for binary, 0o for octal, 0x for hex in many programming languages
Byte Boundaries
Common sizes: 8-bit (1 byte), 16-bit (2 bytes), 32-bit (4 bytes), 64-bit (8 bytes)
Understanding Number Systems
Number systems are fundamental to computing. Every digital computer uses binary (base 2) internally, but programmers often work with hexadecimal (base 16) for compactness and octal (base 8) for certain applications. Understanding how to convert between these systems is essential for programming, networking, and hardware work.
Common Number Bases
The four main number bases used in computing:
- Binary (Base 2): Digits 0-1. Example: 1010 = 10 in decimal
- Octal (Base 8): Digits 0-7. Example: 12 = 10 in decimal
- Decimal (Base 10): Digits 0-9. Standard numbering system
- Hexadecimal (Base 16): Digits 0-9, A-F. Example: A = 10 in decimal
Conversion Methods
Common conversion techniques:
- Binary to Decimal: Sum of (bit × 2^position)
- Decimal to Binary: Repeated division by 2, collect remainders
- Binary to Hex: Group by 4 bits, convert each group
- Binary to Octal: Group by 3 bits, convert each group
- Hex to Binary: Each hex digit → 4 binary bits
Why Hexadecimal?
Hexadecimal is widely used because:
- Compact: Each hex digit = 4 binary bits
- Readable: Easier than long binary strings
- Byte-aligned: 2 hex digits = 1 byte (8 bits)
- Web colors: #RRGGBB format
- Memory addresses: Typically shown in hex
Using This Converter
Follow these steps:
- Step 1: Select the input base (Binary, Octal, Decimal, or Hex)
- Step 2: Enter your number in the selected base
- Step 3: See instant conversion to all four bases
- Step 4: View the bit visualizer showing binary representation
- Step 5: Check statistics (bit count, ones/zeros count)
- Step 6: Click on any result to copy to clipboard
- Step 7: Try bitwise operations in the Bitwise Ops tab
- Step 8: Explore the ASCII table in the ASCII tab
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