Calculadora Binaria
Convierte decimal a binario y realiza aritmética binaria
Binary Calculator
Convert between decimal and binary
Enter a decimal integer
Divide by 2 repeatedly and read remainders bottom-to-topWhat is a Binary Calculator?
A Binary Calculator is a tool for working with binary numbers, which are numbers written using only two digits: 0 and 1. Binary is the fundamental number system used by computers because digital circuits naturally represent two states (off/on, low/high, 0/1).
Binary numbers follow the same place-value concept as decimal numbers, but instead of powers of 10, binary uses powers of 2. For example, the binary number 1011₂ means: 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11 in decimal.
This Calculator Supports Multiple Conversions
- Decimal → Binary -- convert base-10 numbers to base-2
- Decimal → Octal -- convert base-10 numbers to base-8
- Decimal → Hexadecimal -- convert base-10 numbers to base-16
Binary calculators are useful for converting between number bases, understanding computer science topics like bits, bytes, and data representation, and working with hexadecimal (base 16), which is commonly used to represent binary compactly.
How to Use This Binary Calculator
- Enter a decimal number -- type any integer into the input field (e.g., 255)
- Click "Calculate" -- to convert the number
- Review all three outputs -- the result shows the binary (base 2), octal (base 8), and hexadecimal (base 16) representations simultaneously
- Try other values -- explore powers of 2, common byte values (128, 255, 256), or any number you need to convert
Tips:
- A valid binary number contains only 0 and 1 (no digits 2 through 9)
- Leading zeros (like 00101) don't change the value, but they can be useful for showing fixed bit-length formats
- Hexadecimal uses digits 0–9 and letters A–F (where A=10, B=11, …, F=15)
Binary Formulas
Binary Place Value
A binary number has digits (bits) with place values based on powers of 2:
2⁰, 2¹, 2², 2³, 2⁴, …
For binary number bₖbₖ₋₁…b₁b₀, the decimal value is:
value = Σ bᵢ × 2ⁱ (i = 0 to k)
where each bᵢ is either 0 or 1
Converting Decimal to Binary
Repeatedly divide by 2 and record remainders:
- Divide the number by 2
- Record the remainder (0 or 1)
- Divide the quotient by 2 and repeat until the quotient is 0
- Read the remainders from bottom to top
Binary Addition Rules
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10
0 carry 1
Example Calculations
Example 1: Convert Binary to Decimal
Convert: 1011₂ to decimal
Calculation: 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1
Result: 1011₂ = 11₁₀
Example 2: Convert Decimal to Binary
Convert: 13₁₀ to binary
Steps:
- 13 ÷ 2 = 6 remainder 1
- 6 ÷ 2 = 3 remainder 0
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
Read upward: 1101
Result: 13₁₀ = 1101₂
Example 3: Binary Addition
Add: 1011₂ + 0101₂
Calculation: 1011 + 0101 = 10000
Verify: 11 + 5 = 16 in decimal
Result: 1011₂ + 0101₂ = 10000₂
Example 4: Binary Multiplication
Multiply: 101₂ × 11₂
In decimal: 5 × 3 = 15
15 in binary: 1111₂
Result: 101₂ × 11₂ = 1111₂
Frequently Asked Questions
Why do computers use binary instead of decimal?
Computers are built from electronic components that naturally represent two states (on/off). Binary matches this perfectly, making it reliable and efficient for hardware design.
What is a bit and a byte?
A bit is a single binary digit (0 or 1). A byte is typically 8 bits, which can represent 256 different values (0–255).
What's the difference between binary and hexadecimal?
Hexadecimal (base 16) is a compact way to write binary. Every 4 binary bits corresponds to one hex digit (0–9 and A–F). For example, 1111₂ = F₁₆.
Can binary numbers represent negative values?
Yes. Computers often use formats like two's complement to represent negative numbers in binary. Some binary calculators support this, but many basic tools focus on non-negative integers.
Why do binary results sometimes look "long"?
Because binary uses only 0 and 1, it needs more digits to represent large numbers. For example, 255₁₀ is 11111111₂, which is 8 bits long.
Want to add this binary calculator to your website? Get a custom embed code that matches your site's design and keeps visitors engaged.
¿Qué es el sistema numérico binario?
El binario es el sistema de numeración en base 2 que utiliza únicamente dos dígitos: 0 y 1. Toda la información digital — texto, imágenes, video, programas — se almacena en última instancia como secuencias de dígitos binarios (bits). Entender el binario es fundamental para la informática y la electrónica digital. A nivel de hardware, el 0 y el 1 corresponden directamente a los estados apagado y encendido de los transistores, lo que hace del binario el lenguaje nativo de cualquier procesador.
Esta calculadora convierte entre decimal (el sistema cotidiano en base 10) y binario, y puede realizar sumas y restas binarias. También muestra los equivalentes en octal (base 8) y hexadecimal (base 16), para que puedas ver cómo luce el mismo valor en los sistemas numéricos más usados en informática y programación.
Cómo usar la calculadora binaria
- Ingresa un número decimal para convertirlo a binario, o un número binario (solo dígitos 0 y 1) para convertirlo a decimal.
- Selecciona la dirección de conversión: Decimal → Binario o Binario → Decimal.
- Haz clic en Calcular para ver el resultado.
- Lee el resultado binario junto con sus equivalentes en octal y hexadecimal que se muestran a continuación.
Fórmulas de conversión
Decimal a binario: divide entre 2 y recoge los residuos (LSB primero)
Ejemplo: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1
Lee los residuos de abajo hacia arriba: 13₁₀ = 1101₂
Binario a decimal: multiplica cada bit por 2^posición
1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8+4+0+1 = 13
Suma binaria: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (acarreo 1)Los bits se numeran de derecha a izquierda comenzando en 0. El bit más a la izquierda es el Bit Más Significativo (MSB); el más a la derecha es el Bit Menos Significativo (LSB).
Ejemplos resueltos
42₁₀ = 101010₂
Divide 42 repetidamente entre 2: 42→21 R0, 21→10 R1, 10→5 R0, 5→2 R1, 2→1 R0, 1→0 R1. Leyendo los residuos de abajo hacia arriba se obtiene 101010. Verificación: 32+8+2 = 42.
11111111₂ = 255₁₀ (valor máximo de 8 bits)
Ocho bits en 1 = 128+64+32+16+8+4+2+1 = 255. Este es el valor máximo que puede almacenar un byte sin signo de 8 bits, razón por la cual los octetos de una dirección IP van de 0 a 255.
1010₂ + 0110₂ = 10000₂ (suma binaria: 10 + 6 = 16)
Suma columna por columna de derecha a izquierda: 0+0=0, 1+1=10 (escribe 0 acarreo 1), 0+1+1=10 (escribe 0 acarreo 1), 1+0+1=10 (escribe 0 acarreo 1). El 1 acarreado se convierte en el bit inicial: resultado 10000₂ = 16₁₀.