What is Binary?
Binary is a base-2 number system that uses only two digits: 0 and 1. While humans count in base 10 (using digits 0–9), computers use binary because electronic circuits can easily represent two states: on (1) and off (0).
How to Convert Binary to Decimal
Each position in a binary number represents a power of 2, starting from the right (2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8, and so on). To convert, multiply each digit by its position value and add them all up.
Example: 1011 in binary
- 1 × 2^3 = 8
- 0 × 2^2 = 0
- 1 × 2^1 = 2
- 1 × 2^0 = 1
- Total: 8 + 0 + 2 + 1 = 11 in decimal
How to Convert Decimal to Binary
Divide the number by 2 repeatedly and record the remainders. Read the remainders from bottom to top.
Example: 13 in decimal
- 13 ÷ 2 = 6 remainder 1
- 6 ÷ 2 = 3 remainder 0
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
- Read bottom to top: 1101
Common Binary Values to Memorize
- 0000 = 0 0001 = 1 0010 = 2 0011 = 3
- 0100 = 4 0101 = 5 0110 = 6 0111 = 7
- 1000 = 8 1001 = 9 1010 = 10 1111 = 15
- 11111111 = 255 (8 bits / 1 byte max)
Use our free binary converter to convert between decimal, binary, hex and octal instantly.
Frequently Asked Questions
How do I convert binary to decimal by hand?
Write down each binary digit and multiply it by its positional value (powers of 2 from right to left: 1, 2, 4, 8, 16...). Add up the results. Example: 1101 = (1×8) + (1×4) + (0×2) + (1×1) = 8+4+0+1 = 13. Our converter handles this instantly for any size number.
Why do computers use binary?
Computers use binary because electronic circuits naturally operate in two states: on (1) or off (0). Using a two-state system makes hardware simpler, more reliable, and less error-prone than trying to represent ten distinct voltage levels for a decimal system. Every program, image, and file on your computer is ultimately stored as binary.
What is the largest number you can represent with 8 bits?
With 8 bits (one byte), you can represent numbers from 0 to 255 (2⁸ − 1 = 255). For signed integers (positive and negative), the range is −128 to +127. This is why IPv4 addresses have values from 0 to 255 in each octet — each octet is exactly one byte.
Convert between decimal, binary, hexadecimal, and octal instantly.
⚡ Binary & Number Systems Converter — FreeAccuracy note: Conversion factors on SwiftConvertHub are sourced from NIST and IEC standards. Results are accurate for general use. For safety-critical or professional applications, verify results independently. Full disclaimer →
Victor A. Calvo S. is a software engineer and digital entrepreneur who builds practical, free tools for developers, students, and professionals worldwide. He is the creator of SwiftConvertHub, InstantLinkHub, and Feexio. All conversion factors are cross-referenced against NIST and IEC standards. Learn more →