⚡ Quick Answer

Convert between Binary (base 2), Decimal (base 10), Hexadecimal (base 16), and Octal (base 8). Example: decimal 255 = binary 11111111 = hexadecimal FF = octal 377. Binary uses only 0 and 1. Computers store all data in binary because electronic circuits have two states: on (1) and off (0).

📂 Math

💻 Binary Number Converter

Convert numbers between binary, decimal, hexadecimal, and octal instantly. Perfect for computer science students, programmers, and electronics enthusiasts.

✏️ Enter Your Values

💻 Input Number System 🔢 Enter Number

✨ Your Result

🦉Owl's Explanation

💻

Fill in the values above and click Calculate ✨

✅ Trusted Tool

The 365tool.net Binary Converter handles all standard integer number base conversions accurately. For very large numbers, JavaScript floating-point precision applies. Free for students, programmers, and electronics enthusiasts. No sign-up needed.

🤔 How Does This Work?

The Binary Converter uses JavaScript's parseInt() and toString():

Convert input to decimal: parseInt(value, fromBase)
Convert decimal to each target base: number.toString(toBase)
Handles binary (2), decimal (10), hex (16), and octal (8)
Validates input contains only valid digits for the selected base

❓ Frequently Asked Questions

Why do computers use binary?▼

Computers use binary because electronic components (transistors) naturally have two states: on (1) and off (0). Building reliable circuits for 10 states (decimal) is far more complex and error-prone. Binary makes electronics simpler, faster, and more reliable. All computer data — text, images, videos, programs — is ultimately stored as sequences of 0s and 1s.

What is hexadecimal used for?▼

Hexadecimal (base 16, using 0-9 and A-F) is a compact way to represent binary. Each hex digit represents exactly 4 binary bits. So 1 byte (8 bits) = 2 hex digits. Programmers use hex for: memory addresses (0x7FFF0000), color codes in web design (#FF6B9D), ASCII and Unicode values, error codes, and debugging. It is more readable than long binary strings.

What is a bit and a byte?▼

A bit is the smallest unit of data — either 0 or 1. A byte is 8 bits and can represent 256 different values (0-255 in decimal, 00-FF in hex, 00000000-11111111 in binary). Common sizes: 1 Kilobyte = 1,024 bytes, 1 Megabyte = 1,024 KB, 1 Gigabyte = 1,024 MB, 1 Terabyte = 1,024 GB.

How do I convert binary to decimal?▼

Multiply each binary digit by 2 raised to its position (from right, starting at 0), then add all results. Example: 1011 = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 in decimal. Our converter shows this step-by-step.

What is two's complement?▼

Two's complement is how computers represent negative numbers in binary. To negate a binary number: flip all bits (0→1, 1→0), then add 1. This allows the same circuits to perform addition and subtraction. In an 8-bit system: 0 to 127 are positive (00000000-01111111), -128 to -1 are negative (10000000-11111111).