Binary Binary Calculator

Binary Arithmetic Calculator

This calculator performs basic arithmetic operations (addition, subtraction, multiplication, and division) on two binary numbers. Enter your binary numbers, select an operation, and get the result in binary.

Understanding Binary Numbers and Arithmetic

Binary numbers are the fundamental language of computers. Unlike the decimal system (base-10) we use daily, which employs ten digits (0-9), the binary system (base-2) uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from 2^0 on the rightmost side.

How Binary Numbers Work

For example, the binary number 10110 can be converted to decimal as follows:

• 1 * 2^4 (16)
• 0 * 2^3 (0)
• 1 * 2^2 (4)
• 1 * 2^1 (2)
• 0 * 2^0 (0)

Adding these values: 16 + 0 + 4 + 2 + 0 = 22. So, 10110 in binary is 22 in decimal.

Binary Arithmetic Operations

Performing arithmetic operations directly in binary can be done using specific rules for each operation, similar to how we do it in decimal. However, for complex calculations, it's often easier to convert the binary numbers to their decimal equivalents, perform the operation, and then convert the result back to binary. This calculator uses this method to ensure accuracy and handle various scenarios.

Addition (+)

Binary addition follows simple rules: 0+0=0, 0+1=1, 1+0=1, and 1+1=0 with a carry-over of 1. For example, 101 + 11 = 1000 (5 + 3 = 8).

Subtraction (-)

Binary subtraction can be more complex, often involving borrowing. A common method in computers is using two's complement for negative numbers. For simplicity, this calculator performs subtraction by converting to decimal, subtracting, and then converting the absolute value back to binary, prepending a minus sign if the result is negative. For example, 10110 - 1101 = 1011 (22 – 13 = 9).

Multiplication (*)

Binary multiplication is similar to decimal multiplication, involving shifts and additions. For example, 101 * 11 = 1111 (5 * 3 = 15).

Division (/)

Binary division is also analogous to long division in decimal. This calculator performs integer division, meaning it will provide the whole number part of the quotient. For example, 10110 / 1101 = 1 (22 / 13 = 1 with a remainder).

How to Use the Calculator

1. Enter your first binary number into the "Binary Number 1" field.
2. Enter your second binary number into the "Binary Number 2" field.
3. Select the desired arithmetic operation from the "Operation" dropdown.
4. Click the "Calculate" button to see the result in binary.

Examples

• Addition: If Binary Number 1 is 10110 (22) and Binary Number 2 is 1101 (13), selecting Addition will yield 100011 (35).
• Subtraction: If Binary Number 1 is 10110 (22) and Binary Number 2 is 1101 (13), selecting Subtraction will yield 1011 (9).
• Multiplication: If Binary Number 1 is 10110 (22) and Binary Number 2 is 1101 (13), selecting Multiplication will yield 100011110 (286).
• Division: If Binary Number 1 is 10110 (22) and Binary Number 2 is 1101 (13), selecting Division will yield 1 (1).