Step-by-Step Instructions

1. 1.
   Enter First Binary Number: Input your first binary number using only 0s and 1s. The calculator validates input to ensure proper binary format.
2. 2.
   Enter Second Binary Number: Input your second binary number. Both numbers can be of different lengths for flexible calculations.
3. 3.
   Select Operation: Choose from arithmetic operations (add, subtract, multiply, divide) or logical operations (AND, OR, XOR) based on your calculation needs.
4. 4.
   Calculate and Review: Click calculate to see the binary result, decimal equivalent, and detailed step-by-step solution process.

Calculator Features

How do you add binary numbers?

Binary addition follows the same rules as decimal addition but with only two digits (0 and 1). When adding 1 + 1, the result is 0 with a carry of 1 to the next position. Our binary calculator shows this process step-by-step.

What is the difference between binary and decimal?

Decimal uses base-10 with digits 0-9, while binary uses base-2 with only 0 and 1. Each position in binary represents a power of 2, while decimal positions represent powers of 10.

How do you convert binary to decimal?

To convert binary to decimal, multiply each binary digit by 2 raised to its position power (starting from 0 on the right) and sum all results. For example, 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 11₁₀.

What are logical operations in binary?

Logical operations (AND, OR, XOR) compare corresponding bits of two binary numbers. AND returns 1 only if both bits are 1, OR returns 1 if either bit is 1, and XOR returns 1 if bits are different.

Why is binary important in computers?

Binary is fundamental to computers because electronic circuits have two states: on (1) and off (0). All computer data, instructions, and operations are ultimately processed in binary form.

How do you subtract binary numbers?

Binary subtraction uses borrowing similar to decimal subtraction. When subtracting 1 from 0, you borrow 1 from the next higher position, making it 2 in binary, then 2-1=1.

What is binary multiplication?

Binary multiplication is simpler than decimal multiplication since you only multiply by 0 or 1. The result is either 0 (if multiplying by 0) or the original number (if multiplying by 1), then shifted and added.

How are negative numbers represented in binary?

Negative numbers in binary use two's complement representation, where the leftmost bit indicates sign (0 for positive, 1 for negative) and the value is inverted and incremented.