Computers store and process all information using binary—a number system that has only two digits: 0 and 1. These digits are called bits (binary digits). One bit represents two possibilities, but combining many bits allows representation of very large ranges of values and many types of data.
Digital circuits are designed around two reliable states:
Using two states is efficient and resistant to noise, which is why binary is the foundation of computing.
Binary is a positional system like decimal. Each position is a power of 2:
| Place | 2³ | 2² | 2¹ | 2⁰ |
|---|---|---|---|---|
| Value | 8 | 4 | 2 | 1 |
Example: 1101₂ = (1×8) + (1×4) + (0×2) + (1×1) = 13₁₀.
Binary is a universal internal representation:
| Data Type | How Binary Is Used |
|---|---|
| Numbers | Integers and real numbers (e.g., floating point) |
| Text | Character codes like ASCII and Unicode |
| Images | Pixel color values (e.g., RGB channels) |
| Sound | Sampled amplitudes over time |
Key idea: Regardless of what you see (text, photos, audio), the underlying storage and processing is bits.
| Term | Meaning |
|---|---|
| Bit | A single 0 or 1 |
| Byte | 8 bits |
| Base-2 | The numbering system of binary |
| Base-10 | Decimal (everyday human system) |
| Overflow | When a value is too large for the allotted bits |
With only 4 bits, the largest value is 1111₂ = 15₁₀.
Trying to store 16 (which is 10000₂) requires 5 bits—so in 4 bits this causes overflow.
Binary is the fundamental way computers encode any type of information because hardware naturally supports two stable states. Understanding bits, place value, and overflow prepares you to reason about data, storage, and limits in computing systems.