### What is Binary?

**Binary** is a base-2 number system, meaning it uses only two digits: 0 and 1. Each digit in a binary number is called a “bit,” which is short for “binary digit.”

### How Binary Works

**Place Values:**

- Just like in the decimal system (base-10), where place values are powers of 10 (1, 10, 100, etc.), binary place values are powers of 2.
- For example, in binary, the place values from right to left are (2^0), (2^1), (2^2), (2^3), and so on.

**Binary Digits:**

- Each digit in a binary number represents a power of 2. For instance, in the binary number
`1101`

, the place values are:`1 1 0 1 2^3 2^2 2^1 2^0`

**Converting Binary to Decimal:**

- To convert a binary number to a decimal number, multiply each binary digit by its corresponding power of 2 and then add the results together. For example, converting
`1101`

to decimal:- (1 \times 2^3 = 8)
- (1 \times 2^2 = 4)
- (0 \times 2^1 = 0)
- (1 \times 2^0 = 1)
- Adding these gives (8 + 4 + 0 + 1 = 13) So,
`1101`

in binary is`13`

in decimal.

**Binary Arithmetic:**

- Binary addition and subtraction are similar to decimal but simpler because you only work with 0s and 1s. For instance:
**Binary Addition:**`1 1 0 (6 in decimal) + 1 0 1 (5 in decimal) ------ 1 0 0 1 (11 in decimal)`

**Binary Subtraction:**`1 0 1 0 (10 in decimal) - 0 1 1 1 (7 in decimal) ------ 0 1 1 1 (3 in decimal)`

**Applications of Binary:**

**Computing:**All modern computers use binary because it’s simpler to design electronic circuits that only have two states: on (1) and off (0).**Data Storage:**Binary is used to represent data in memory, files, and other forms of digital storage.**Digital Communications:**Binary is also used in digital communication systems for transmitting data.

### Example

Let’s convert the binary number `1010`

to decimal:

- (1 \times 2^3 = 8)
- (0 \times 2^2 = 0)
- (1 \times 2^1 = 2)
- (0 \times 2^0 = 0)

Adding these values gives (8 + 0 + 2 + 0 = 10). So, `1010`

in binary equals `10`

in decimal.

Binary is essential for understanding how computers process and store data. If you have more questions about binary or related topics, feel free to ask!

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