Number System Converter
Convert between different number systems and ASCII characters
Result
Conversion Formulas [ascii table]
Binary to Decimal (Bin to Dec)
Multiply each digit by 2 raised to its position power:
(bn...b₃b₂b₁b₀)₂ = b₀×2⁰ + b₁×2¹ + b₂×2² + b₃×2³ + ... + bn×2ⁿ
Example: 1010₂ = (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 10₁₀
Binary to Octal (Bin to Oct)
Group binary digits into sets of three from right to left:
1010110₂ = 001|010|110₂ = 1|2|6₈ = 126₈
Example: 1010110₂ = 126₈
Binary to Hexadecimal (Bin to Hex)
Group binary digits into sets of four from right to left:
1010110₂ = 0101|0110₂ = 5|6₁₆ = 56₁₆
Example: 1010110₂ = 56₁₆
Octal to Binary (Oct to Bin)
Convert each octal digit to 3 binary digits:
126₈ = 001|010|110₂ = 1010110₂
Example: 126₈ = 1010110₂
Octal to Decimal (Oct to Dec)
Multiply each digit by 8 raised to its position power:
(on...o₃o₂o₁o₀)₈ = o₀×8⁰ + o₁×8¹ + o₂×8² + o₃×8³ + ... + on×8ⁿ
Example: 126₈ = (1×8²) + (2×8¹) + (6×8⁰) = 86₁₀
Octal to Hexadecimal (Oct to Hex)
First convert to binary, then to hexadecimal:
126₈ = 1010110₂ = 56₁₆
Example: 126₈ = 56₁₆
Decimal to Binary (Dec to Bin)
Divide by 2 and record remainders:
10₁₀ = 1010₂ (10 ÷ 2 = 5 R0, 5 ÷ 2 = 2 R1, 2 ÷ 2 = 1 R0, 1 ÷ 2 = 0 R1)
Example: 10₁₀ = 1010₂
Decimal to Octal (Dec to Oct)
Divide by 8 and record remainders:
86₁₀ = 126₈ (86 ÷ 8 = 10 R6, 10 ÷ 8 = 1 R2, 1 ÷ 8 = 0 R1)
Example: 86₁₀ = 126₈
Decimal to Hexadecimal (Dec to Hex)
Divide by 16 and record remainders:
86₁₀ = 56₁₆ (86 ÷ 16 = 5 R6)
Example: 86₁₀ = 56₁₆
Hexadecimal to Binary (Hex to Bin)
Convert each hex digit to 4 binary digits:
56₁₆ = 0101|0110₂ = 1010110₂
Example: 56₁₆ = 1010110₂
Hexadecimal to Octal (Hex to Oct)
First convert to binary, then to octal:
56₁₆ = 1010110₂ = 126₈
Example: 56₁₆ = 126₈
Hexadecimal to Decimal (Hex to Dec)
Multiply each digit by 16 raised to its position power:
(hn...h₃h₂h₁h₀)₁₆ = h₀×16⁰ + h₁×16¹ + h₂×16² + h₃×16³ + ... + hn×16ⁿ
Example: 56₁₆ = (5×16¹) + (6×16⁰) = 86₁₀
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Number System Converter Guide
Multiple Number Systems
Convert between binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16), and ASCII characters. Support for both positive and negative numbers.
Character Conversion
Convert between characters and their numerical representations. Support for ASCII and Unicode character sets. Useful for programming and data encoding.
Real-time Conversion
Instant conversion with detailed explanations. Copy results with a single click. Clear error messages for invalid inputs.
Number System Basics
- Binary (Base 2): Uses digits 0 and 1
- Octal (Base 8): Uses digits 0-7
- Decimal (Base 10): Uses digits 0-9
- Hexadecimal (Base 16): Uses digits 0-9 and letters A-F
- Character: ASCII and Unicode character representations
Conversion Tips
- Binary numbers should start with '0b' (optional)
- Hexadecimal numbers should start with '0x' (optional)
- Octal numbers should start with '0' (optional)
- For character conversion, enter a single character or its ASCII code
- Use the copy button to easily transfer results