Numeral Systems Converter – Binary, Decimal, Hexadecimal, Octal & Roman Numerals

Imagine you’re working on a coding project, solving a math problem, or just curious about how numbers are represented differently in computing and history. You see 1010 in binary, A in hexadecimal, or X in Roman numerals — and you wonder how they connect. That’s exactly what a Numeral Systems Converter does: it instantly changes numbers from one system to another, helping you understand, calculate, and communicate with clarity.

This guide walks you through what the converter does, why it matters, the formulas behind the systems, step-by-step usage, and answers to the most common questions.

Why Numeral System Conversion Matters

Numbers aren’t always written the same way. Each system has its own purpose:

• Binary (base-2): The language of computers — only 0 and 1.
  
• Decimal (base-10): Everyday human numbers — 0–9.
  
• Hexadecimal (base-16): Used in programming, memory addresses, colors in web design — 0–9 + A–F.
  
• Octal (base-8): Older computing, file permissions in Unix/Linux — 0–7.
  
• Roman numerals: Ancient system still seen on clocks, buildings, book chapters, and events.
  

Being able to switch between them quickly is useful for students, programmers, engineers, and anyone interested in mathematics.

What You Can Do With This Converter

The converter lets you:

• Change binary to decimal, hexadecimal, or octal.
  
• Change decimal to binary, hexadecimal, or octal.
  
• Convert hexadecimal to decimal, binary, or octal.
  
• Work with Roman numerals to convert back and forth with decimal numbers.
  

No memorization of rules needed — the tool handles it instantly.

Conversion Rules & Formulas

Here’s the logic behind the conversions:

• Binary to Decimal: Multiply each bit by powers of 2, from right to left.
  Example: 1010₂ = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 10₁₀.
  
• Decimal to Binary: Divide the number by 2 repeatedly, noting remainders.
  Example: 10₁₀ = 1010₂.
  
• Decimal to Hexadecimal: Divide by 16, use remainders (0–9, A–F).
  Example: 255₁₀ = FF₁₆.
  
• Decimal to Octal: Divide by 8, note remainders.
  Example: 64₁₀ = 100₈.
  
• Roman Numerals: Use additive and subtractive rules with symbols (I, V, X, L, C, D, M).
  Example: 2025 = MMXXV.
  

How the Converter Works

Converting Binary ➝ Decimal

1. Enter your binary number (like 1011).
   
2. The tool multiplies each digit by powers of 2.
   
3. Result: 1011₂ = 11₁₀.
   

Converting Decimal ➝ Hexadecimal

1. Enter a decimal (like 255).
   
2. The tool divides by 16 until 0, collecting remainders.
   
3. Result: 255₁₀ = FF₁₆.
   

Converting Decimal ➝ Octal

1. Enter decimal (like 64).
   
2. Divide by 8 repeatedly.
   
3. Result: 64₁₀ = 100₈.
   

Converting Decimal ➝ Roman

1. Enter decimal (like 1984).
   
2. The tool subtracts largest Roman numeral values step by step.
   
3. Result: 1984 = MCMLXXXIV.