Number System Converter
Convert between Binary, Decimal, Hexadecimal & Octal — all at once, instantly.
Number System Converter – Complete Guide to Number Bases
At the heart of all digital technology lies a deceptively simple concept: number systems. Every file on your computer, every website you visit, every digital image you see — all of it is ultimately represented as numbers in different bases. Understanding these number systems is fundamental to computer science, electronics, networking, and programming. Arattai.it.com's free Number System Converter lets you instantly convert between Decimal, Binary, Hexadecimal, Octal, and any custom base from 2 to 36.
The Four Major Number Systems
Decimal (Base 10)
Decimal is the number system we use in everyday life. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Each position represents a power of 10. The number 425 means (4 × 10²) + (2 × 10¹) + (5 × 10⁰) = 400 + 20 + 5 = 425. Humans use decimal likely because we have 10 fingers.
Binary (Base 2)
Binary is the fundamental language of computers. It uses only two digits: 0 and 1. Each position represents a power of 2. The binary number 1011 means (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = 8 + 0 + 2 + 1 = 11 in decimal. Everything inside a computer — from text to images to videos — is stored as sequences of 0s and 1s (bits).
Hexadecimal (Base 16)
Hexadecimal (hex) uses 16 symbols: 0–9 and A–F (where A=10, B=11, C=12, D=13, E=14, F=15). Hex is widely used in programming because one hex digit represents exactly 4 binary bits, making it a compact notation for binary data. A byte (8 bits) is represented by just two hex digits — for example, 255 decimal = FF hex = 11111111 binary. HTML color codes like #FF6B6B use hexadecimal.
Octal (Base 8)
Octal uses digits 0–7. Each octal digit represents 3 binary bits. While less common today, octal was historically important in early computing. Unix/Linux file permissions use octal — the permission 755 (rwxr-xr-x) is a classic example that every sysadmin knows.
How to Convert Between Number Systems
Decimal to Binary
Divide the decimal number by 2 repeatedly, recording remainders. Read remainders from bottom to top. Example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1 → Binary: 1101.
Binary to Decimal
Multiply each bit by its positional power of 2 and sum. 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 8+4+0+1 = 13.
Decimal to Hexadecimal
Divide by 16 repeatedly, recording remainders (using A–F for values 10–15). Read from bottom to top. Example: 255 ÷ 16 = 15 R15 (F), 15 ÷ 16 = 0 R15 (F) → FF.
Real-World Applications
- Web Development: HTML/CSS color codes in hexadecimal (#RRGGBB)
- Networking: IP addresses, MAC addresses, subnet masks
- Cryptography: Hash values (SHA-256 output in hex), encryption keys
- Assembly Language: Memory addresses and opcodes in hex
- File Systems: File headers, magic numbers, binary file analysis
- Electronics: Register values on microcontrollers (Arduinos, PICs)
- Databases: UUID/GUID storage and bit masking operations
ASCII and Character Encoding
The ASCII standard assigns a decimal number to every common character. 'A' = 65 decimal = 41 hex = 1000001 binary. 'a' = 97 decimal = 61 hex = 1100001 binary. Understanding number conversions helps decode text from binary or hex representations — a skill essential in cybersecurity and low-level programming.
Why Use Arattai.it.com Number System Converter?
Our tool updates all four number system fields simultaneously as you type in any one of them — no button press needed. The custom base converter supports any base from 2 to 36, covering unusual bases like base 3 (ternary), base 12 (duodecimal), and base 36 (alphanumeric). The monospace font display makes reading binary and hex much easier. The interface is designed for developers, students, and digital electronics enthusiasts alike.