Hex Calculator Convert between hexadecimal, decimal, binary, and octal number systems — with bitwise operations and color...

Hex Calculator

Convert between hexadecimal, decimal, binary, and octal number systems — with bitwise operations and color representation.

Base Conversion

Hex Arithmetic

Bitwise Operations

Color Converter

Value to Convert

From Base Hexadecimal Decimal Binary Octal

To Base Decimal Hexadecimal Binary Octal

First Hex

Second Hex

Operation Addition (+) Subtraction (-) Multiplication (×) Division (÷)

First Hex

Second Hex

Operation AND (&) OR (|) XOR (^) NOT (First) NOT (Second) Shift Left (<<) Shift Right (>>)

Shift Bits

Hex Color

Preview

Binary Representation (8-bit)

10100101

A5

Input Value

165

Result

Convert

Operation

Hex → Dec

Conversion

Hexadecimal

A5

Decimal

165

Binary

10100101

Octal

245

Bit Visualization

Hexadecimal Number System

The hexadecimal (base-16) number system uses 16 digits: 0-9 and A-F.

Hex Digits**:

• 0-9**: Same as decimal (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
• A-F**: Represent 10-15 (A=10, B=11, C=12, D=13, E=14, F=15)

Place Values** (right to left):

• 16⁰ = 1 (ones place)
• 16¹ = 16 (sixteens place)
• 16² = 256 (two-hundred-fifty-sixes place)
• 16³ = 4,096 (four-thousand-ninety-sixes place)

Example**: A5₁₆ = (10 × 16¹) + (5 × 16⁰) = 160 + 5 = 165₁₀

✅ Why Hex?**: Hex is used in computing because it's a compact representation of binary (each hex digit = 4 bits).

Common Hex Calculation Mistakes

⚠️ Avoid these frequent errors:

• Invalid characters**: Hex only uses 0-9 and A-F (not G, H, etc.)
• Case sensitivity**: A-F and a-f are both valid, but be consistent
• Leading zeros**: 0A5 is the same as A5 in value, but may matter in some contexts
• Negative numbers**: Standard hex is unsigned; two's complement for negatives
• Overflow**: Results may exceed the maximum displayable hex digits

✅ Best Practices**:

• Always validate hex input before processing
• Use uppercase letters for consistency (A-F instead of a-f)
• Prefix hex values with 0x when clarity is needed (0xA5)
• For color codes, always use 6-digit format (#RRGGBB)

Real-World Applications

Hexadecimal is essential in:

• Web Development**: Color codes (#FF5733), CSS values
• Computer Science**: Memory addresses, machine code, debugging
• Networking**: MAC addresses, IPv6 addresses
• Electronics**: Register values, configuration settings
• Data Representation**: Compact binary data display

📊 Example Use Cases**:

• Web Colors**: #A52A2A = Brown
• Memory Address**: 0x7FFF5FBFF000 (stack pointer in macOS)
• MAC Address**: A5:2A:2A:FF:57:33 (network interface identifier)
• IPv6**: 2001:0db8:85a3:0000:0000:8a2e:0370:7334

How to Use This Calculator

➡️ Base Conversion

"Convert A5 hex to decimal" → 165

➡️ Hex Arithmetic

"A5 + 1B hex" → C0 hex (192 decimal)

➡️ Bitwise Operations

"A5 AND 1B hex" → 01 hex (1 decimal)

➡️ Color Converter

"#A52A2A" → RGB(165, 42, 42), Brown color preview

Note: All hex inputs are case-insensitive. For arithmetic and bitwise operations, inputs are treated as unsigned 32-bit integers.