2. Positional number systems

Positional numbering system

Decimal system

The decimal system is typically used by humans for representing numbers, it is a **base-10** numbering system.

• It uses 10 digits.
• Each position corresponds to $10^n$.
• For example, $123=10^3+(2\times 10^2)+3$.

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Binary

Binary is a **base-2** numbering system.

• It uses two binary digits (bits), typically $1$ and $0$.
• Each position corresponds to $2^n$.
• For example, $1001=2^3+2^0$.

• Byte

  A byte is a series of eight bits.

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• Nibble

  A nibble is a series of four bits.

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Radix notation

Radix notation is a way we write numbers to distinguish different bases.

• $10010_{10}$ is a decimal number.
• $10010_2$ is a binary number.

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Prefix notation

We can also use prefix notation, we indicate the base preceding the number:

• $0\text{b}010101$ is a binary number.
• $0\text{xFF}$ is a Hexadecimal number.

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