Unit Conversions

Number System Converter

Convert numbers between decimal (base-10), binary (base-2), octal (base-8), and hexadecimal (base-16) systems.

✓ Runs in your browser · Updated 2026-03-31

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Convert numbers between decimal (base-10), binary (base-2), octal (base-8), and hexadecimal (base-16) systems.

Updated: 2026-03-31

Number Systems Explained

A number system defines how we represent quantities using symbols. The four common systems are:

  • Decimal (Base 10): Uses digits 0–9. This is the everyday system we use for counting and arithmetic.
  • Binary (Base 2): Uses only 0 and 1. This is the language of computers — every piece of data is ultimately stored as binary.
  • Octal (Base 8): Uses digits 0–7. Commonly used in Unix/Linux file permissions (e.g., chmod 755).
  • Hexadecimal (Base 16): Uses 0–9 and A–F. Widely used in programming for colours (#FF5733), memory addresses, and compact binary representation.

Common Values Reference

DecimalBinaryOctalHexContext
0000Zero / FALSE
1111One / TRUE
10101012A—
12711111111777FMax signed byte
25511111111377FFMax unsigned byte / CSS colour channel
2561000000004001001 byte overflow
755101111001113632F3Common Linux permission
655351111111111111111177777FFFFMax 16-bit value

Use in Programming

Programmers use hexadecimal to write memory addresses (0x7FFF), CSS colours (#00FF00 = green), and byte values compactly. Binary is essential for understanding bitwise operations, flags, and low-level hardware. In India's competitive exams (GATE, UGC NET CS), number system conversion is a frequently tested topic.

Related Converters

For data sizes and bits vs bytes, use the Data Storage Converter. For mathematical calculations, check the Percentage Calculator.

Frequently Asked Questions

How do I convert binary to decimal?

Multiply each binary digit by 2 raised to its position power (starting from 0 on the right) and sum them. For example, 1010 in binary = 8 + 0 + 2 + 0 = 10 in decimal.

What is the hexadecimal number system?

Hexadecimal is a base-16 number system using digits 0–9 and letters A–F (where A=10, B=11, ... F=15). It is widely used in programming and web colours.

How do I convert decimal to octal?

Divide the decimal number by 8 repeatedly and record the remainders in reverse order. For example, 65 in decimal = 101 in octal.