What Is the Binary Number System?
The binary number system uses only two digits: 0 and 1. It's the fundamental language of computers and all digital systems, because electronic circuits hold information as two states (present/absent, on/off).
Why Binary?
In a circuit, a line's logic level is either high (1) or low (0). Being two-state is noise-resistant and reliable, so numbers are represented with these two digits too.
Bit and Byte
A single 0 or 1 is called a bit. Eight bits together make a byte, which can express 256 different values from 0 to 255. Computer memory and data are measured in bytes.
Binary-Decimal Conversion
Each bit, from right to left, represents an increasing power of 2. If a bit's value is 1, that power is added to the sum:
| Bit position | 8 | 4 | 2 | 1 |
|---|---|---|---|---|
| Binary: 1011 | 1 | 0 | 1 | 1 |
| Contribution | 8 | 0 | 2 | 1 |
So 1011 (binary) = 8 + 0 + 2 + 1 = 11 (decimal).
Hexadecimal (Hex) Notation
Because binary numbers are long, they're often shortened with hexadecimal: it uses the digits 0–9 and A–F, and each hex digit corresponds to exactly 4 bits (e.g. 1011 = B). That's why addresses and color codes are written in hex.
Common Mistakes
- Counting place values backwards: the rightmost bit is 1 (2⁰), the leftmost the largest; getting the direction wrong gives a wrong result.
- Confusing bit with byte: 1 byte = 8 bits; this difference is critical in data rate/size.
- Reading hex as decimal: "10" hex = 16 decimal; without the base stated, it's confusing.
Frequently Asked Questions
Why do computers use binary?+
How many values is 8 bits?+
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