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

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