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Divisiones en Base 2

Ejercicio 1

División: 101012÷112101012​÷112​

**Convertimos a decimal para verificar (opcional):**

101012=21101012​=21 y 112=3112​=3.

21÷3=721÷3=7, que en binario es 1001210012​.

**División binaria:** se realiza dividiendo los bloques y verificando el residuo.

**Cociente:** 1001210012​.

**Residuo:** 102102​.

**Resultado:** 1001210012​ con residuo 102102​.

Ejercicio 2

División: 110102÷102110102​÷102​

**Convertimos a decimal (opcional):**

110102=26110102​=26 y 102=2102​=2.

26÷2=1326÷2=13, que en binario es 1101211012​.

**División binaria:** seguimos dividiendo.

**Cociente:** 1101211012​.

**Residuo:** 0202​.

**Resultado:** 1101211012​ sin residuo.                                                                                                                                        

The image you've provided shows binary division, where numbers in binary (base 2) are divided in a similar method to decimal division, with the main difference being the base. Here’s a detailed explanation of the example you gave:

### Explanation of Binary Division
1. **Problem Setup**: The binary number `10101₂` is divided by `11₂`.
   - In decimal, `10101₂ = 21₁₀` and `11₂ = 3₁₀`, which confirms that \(21 \div 3 = 7\) and in binary \(7\) is represented as `1001₂`.

2. **Binary Division Steps**:
   - The division process in binary mirrors the long division in decimal.
   - You align the dividend and subtract blocks of the divisor from it as in long division, recording each result below.

3. **Binary Quotient and Remainder**:
   - Quotient: `1001₂`
   - Remainder: `10₂`

### Example Solution Verification
   - We confirm the binary answer:
     - **Quotient in decimal**: `1001₂ = 7₁₀`
     - **Remainder in decimal**: `10₂ = 2₁₀`
   - This is consistent with the binary result.

The document also contains a second division problem, which follows similar steps with `11010₂ ÷ 10₂`.

Would you like further breakdowns or clarification on binary division? Here are five relative questions to deepen your understanding of binary arithmetic:

1. How does binary division differ from decimal division in terms of mechanics?
2. Why is converting binary numbers to decimal helpful for verification?
3. What are the rules for binary subtraction in division steps?
4. How do we handle remainders in binary division?
5. Can this method be extended to division with larger binary numbers?

**Tip**: Practice converting small binary numbers to decimal and back to reinforce understanding.

Divisiones en Base 2

Ejercicio 1

División: 10101₂ ÷ 11₂

Ejercicio 2

División: 11010₂ ÷ 10₂

Explore step-by-step solutions for binary division problems: 10101₂ ÷ 11₂ and 11010₂ ÷ 10₂. This exercise covers essential binary arithmetic and base conversion techniques, perfect for high school students learning about binary operations.

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