2.1.1 Binary representation of data
Why Binary?
All data inside a computer — numbers, text, images, sound, video, program instructions — is stored and processed as binary: sequences of the digits 0 and 1. This is because computers are built from electronic circuits that have only two stable states: on or off (high voltage or low voltage). A single on/off state represents one bit (binary digit).
Binary is a base-2 number system. Unlike denary (base 10), which uses ten digits (0–9), binary uses only two digits: 0 and 1. Every value stored in a computer must ultimately be encoded as a combination of these two symbols.
Why not use more states?
Electronic circuits can reliably distinguish two voltage levels (on/off). Using more levels (e.g. low/medium/high) would require more precise electronics, making circuits more expensive, slower and prone to errors due to electrical interference. Binary's simplicity makes it extremely robust.
Bits and Bytes
| Term | Size | Notes |
|---|---|---|
| Bit | 1 binary digit (0 or 1) | The smallest unit of data |
| Nibble | 4 bits | Half a byte; one hexadecimal digit |
| Byte | 8 bits | The standard unit for storing one character |
With n bits, it is possible to represent 2ⁿ different values. For example:
- 1 bit → 2 values (0 or 1)
- 4 bits → 2⁴ = 16 values (0000 to 1111)
- 8 bits → 2⁸ = 256 values (00000000 to 11111111)
Everything Is Binary
The same physical bits are used to store all types of data. What distinguishes them is how the bit pattern is interpreted:
| Data type | How it is encoded in binary |
|---|---|
| Integers | Positional binary (unsigned or two's complement) |
| Text | Character encoding (ASCII or Unicode) |
| Images | Pixel colour values (bit depth per pixel) |
| Sound | Sampled amplitude values (sample rate and bit depth) |
| Instructions | Machine code operation codes and operands |
The bit pattern 01000001 could mean the integer 65, the character 'A' (ASCII), or a specific instruction to the processor — the interpretation depends on context.
Key Takeaways
- All data is stored as binary (0s and 1s) because electronic circuits have two stable states.
- A bit is one binary digit; a byte is 8 bits.
- n bits can represent 2ⁿ different values.
- The same bit pattern can represent different data types depending on how it is interpreted.