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Introduction: Binary

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### Binary in Computer Programming

Binary is a base-2 numeral system that uses two symbols: 0 and 1. Each digit in
a binary number is called a bit. In computer programming, binary is crucial
because it directly represents the on/off states of a computer's transistors,
allowing for data storage and processing at the hardware level.

#### Example of a Binary Number:

```sh
1011
```

In this example:

- The rightmost bit represents \(2^0\) (1)
- The next bit represents \(2^1\) (2)
- The next bit represents \(2^2\) (4)
- The leftmost bit represents \(2^3\) (8)

So, `1011` in binary is equal to \(1 \times 8 + 0 \times 4 + 1 \times 2 + 1
\times 1 = 11\) in decimal.

#### Relevance in Programming:

- **Memory Management:** Data is stored and managed in binary at the lowest
  level.
- **Data Representation:** Characters, instructions, and addresses are encoded
  in binary.
- **Logical Operations:** Binary logic is the foundation of conditional
  statements and control flow.
- **Efficiency:** Binary operations are computationally efficient, enhancing
  performance.

Understanding binary is fundamental for low-level programming, debugging, and
optimizing code.

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