Number System Conversions: Binary, Hexadecimal, and Roman Numerals Explained

In everyday life, we count in **Base-10 (Decimal)**, likely because we have ten fingers. But computers count in **Base-2 (Binary)**, programmers often use **Base-16 (Hexadecimal)**, and history left us with **Roman Numerals** and **Base-36**.

Let's demystify these numbering systems and learn how to translate values between them.

1. Binary (Base 2)

Binary has only two digits: **0** and **1**. Each place value represents a power of 2:

• Binary `1011` is:
• - (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)
• - 8 + 0 + 2 + 1 = **11** in Decimal.

2. Hexadecimal (Base 16)

Hexadecimal uses 16 digits: **0-9** and **A-F** (where A=10, B=11, C=12, D=13, E=14, F=15). Because 1 Hex digit represents exactly 4 bits of binary data (a "nibble"), Hex is a concise way for developers to write binary memory addresses.

• Hex `1A` is:
• - (1 × 16¹) + (10 × 16⁰)
• - 16 + 10 = **26** in Decimal.

3. Roman Numerals

Ancient Rome used letters to denote values: **I** (1), **V** (5), **X** (10), **L** (50), **C** (100), **D** (500), and **M** (1000). They use additive and subtractive rules (e.g. `IV` is 5 − 1 = 4, while `VI` is 5 + 1 = 6).

Angles: Degrees vs. Radians

Number converters also handle geometry. In math, angles can be measured in two main units: - **Degrees (360°)**: Standard historical unit. - **Radians (2π)**: Used in physics and trigonometry because they relate the angle directly to the arc length of a circle.

To convert:

**Radians = Degrees × (π ÷ 180)**

**Degrees = Radians × (180 ÷ π)**

Try the calculator

Convert numbering systems instantly. Use our Number System & Angle Converter to translate decimal, binary, hex, octal, Roman numerals, and angle units in one click.