At the most fundamental level, every computer, smartphone, and digital device operates using binary — a number system with just two digits: 0 and 1. Understanding it makes the logic of computing significantly clearer, and makes topics like file sizes, colours, network addresses, and permissions genuinely comprehensible rather than mysterious.
Why Binary?
Computers are built from billions of electronic switches (transistors). Each switch has two states: on or off, high voltage or low voltage. This maps perfectly to binary — on = 1, off = 0. Building reliable circuits for a 10-state system (as decimal would require) is vastly more complex. Binary is the natural language of digital electronics, and everything else is built on top of it.
Our Base64 encoder is one practical application of representing binary data in text form. Our URL encoder similarly handles text-binary representation for web contexts.
How Binary Counting Works
In decimal, each digit position represents a power of 10: 345 = (3×100) + (4×10) + (5×1). Binary works identically but with powers of 2. Binary 1011 = (1×8) + (0×4) + (1×2) + (1×1) = 11 in decimal.
Binary positions from right: 1, 2, 4, 8, 16, 32, 64, 128... Each position doubles.
Converting Decimal to Binary
Repeatedly divide by 2 and record remainders; read them bottom-to-top. Convert 13: 13÷2=6 r1 | 6÷2=3 r0 | 3÷2=1 r1 | 1÷2=0 r1. Bottom to top: 1101. Check: 8+4+0+1 = 13 ✓
Bits and Bytes
A bit is one binary digit. A byte is 8 bits, representing 256 possible values (2⁸). One byte encodes one ASCII character. The storage hierarchy: 8 bits = 1 byte | 1,000 bytes = 1 KB | 1,000 KB = 1 MB | 1,000 MB = 1 GB.
Hexadecimal: Binary's Shorthand
Hexadecimal (base-16, digits 0-9 and A-F) provides a compact human-readable form of binary. Each hex digit = exactly 4 bits. That's why colour codes (#FF5733), memory addresses, and file hashes are written in hex — far shorter than equivalent binary strings. 0xFF = 11111111 binary = 255 decimal.
Practical Appearances of Binary
- IP addresses: IPv4 = 32 bits in four groups of 8 (understanding binary makes subnet masks clear)
- File permissions (Unix/Linux): chmod 755 is octal — a compact binary representation of permission flags
- Colour values: #RRGGBB — each pair is a byte (0-255) for red, green, blue
- Network protocols: all packet headers, checksums, and addresses are binary at the hardware level
Further reading: BBC Bitesize covers binary and data representation for GCSE Computer Science. Learn binary at BBC Bitesize Computer Science.