Como Convertir Number Bases

Converting entre numero bases es un/una fundamental skill in computing. Whether tu're working with binary, hexadecimal, octal, o decimal, el/la metodos son systematic y learnable. This guia walks through cada conversion with clear pasos y ejemplos.

Decimal un/una Binary

Method: Repeated Division by 2

1. Divide el/la numero by 2
2. Record el/la remainder (0 o 1)
3. Divide el/la quotient by 2
4. Repeat until quotient es 0
5. Read remainders bottom-un/una-top

Ejemplo: Convertir 156 un/una Binary

Reading bottom-un/una-top: 156₁₀ = 10011100₂

Binary un/una Decimal

Method: Positional Values

1. Write position valores (powers of 2) under cada digit
2. Multiply cada digit by su position valor
3. Suma todo products

Ejemplo: Convertir 10011100 un/una Decimal

Sum: 128 + 16 + 8 + 4 = 156₁₀

Decimal un/una Hexadecimal

Method: Repeated Division by 16

1. Divide por 16, record remainder
2. Convertir remainders 10-15 un/una Un/Una-F
3. Read remainders bottom-un/una-top

Ejemplo: Convertir 748 un/una Hexadecimal

Reading bottom-un/una-top: 748₁₀ = 2EC₁₆

Hexadecimal un/una Decimal

Method: Positional Values

1. Convertir Un/Una-F un/una 10-15
2. Multiply cada digit by su position valor (powers of 16)
3. Suma todo products

Ejemplo: Convertir 2EC un/una Decimal

• 2 × 16² = 2 × 256 = 512
• E (14) × 16¹ = 14 × 16 = 224
• C (12) × 16⁰ = 12 × 1 = 12

Sum: 512 + 224 + 12 = 748₁₀

Binary un/una Hexadecimal

Method: Group y Convertir

1. Group binary digits into sets of 4 (desde right)
2. Pad with leading zeros si needed
3. Convertir cada group un/una su hex digit

Ejemplo: Convertir 10011100 un/una Hexadecimal

• Group: 1001 | 1100
• 1001 = 9
• 1100 = C

Result: 10011100₂ = 9C₁₆

Hexadecimal un/una Binary

Method: Expand Each Digit

1. Convertir cada hex digit un/una 4 binary digits
2. Concatenate el/la resultados

Ejemplo: Convertir Un/Una7F un/una Binary

• Un/Una = 1010
• 7 = 0111
• F = 1111

Result: Un/Una7F₁₆ = 101001111111₂

Octal Conversions

Binary un/una Octal

Group binary digits in sets of 3 (desde right):

• 110 101 011 (add leading zeros: 0 110 101 011)
• 110 = 6, 101 = 5, 011 = 3
• Result: 653₈

Octal un/una Binary

Convertir cada octal digit un/una 3 binary digits:

• 653₈
• 6 = 110, 5 = 101, 3 = 011
• Result: 110101011₂

Decimal un/una Octal

Divide repeatedly by 8, read remainders bottom-un/una-top.

Any Base un/una Any Base

General Method

1. Convertir source un/una decimal (intermediate paso)
2. Convertir decimal un/una target base

Ejemplo: Convertir 3Un/Una₁₆ un/una Octal

Paso 1: Hex un/una Decimal

• 3 × 16 + 10 × 1 = 48 + 10 = 58₁₀

Paso 2: Decimal un/una Octal

• 58 ÷ 8 = 7 remainder 2
• 7 ÷ 8 = 0 remainder 7
• Result: 72₈

3Un/Una₁₆ = 72₈

Referencia rapida Resumen

Conclusion

Converting entre numero bases follows systematic metodos: division for decimal un/una otro bases, positional multiplication for otro bases un/una decimal, y grouping shortcuts for binary/hex/octal conversiones. With practice, estos conversiones become segundo nature. El/La binary-hex shortcut (4 bits per hex digit) es particularly valuable in programming y computing contexts.

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