Binary Calculator

What is a Binary System?

The binary number system is a system of numbers which operates similar to the decimal system. In the decimal number system, the digit 10 is used as its base. However, in the binary system, the number 2 is used as a base. Additionally, in the decimal system, the numbers 0 to 9 are used. In the binary system, only two numbers are used which includes 0 and 1—every number is referred to as a bit. All other computations are done the same way as in the decimal system.

The latest computer technology is based entirely on the binary number system. Binary can be easily executed in the internal wiring and mechanism of computer systems. The designing of hardware is not difficult at all because they only need to take into consideration two scenarios: either switched on or switched off (same as true or false, 1 or 0, positive or negative). This makes binary ideal for digital electronics and computing.

Our free binary calculator makes it easy to perform addition, subtraction, multiplication, and division operations on binary numbers without manual calculations. Simply enter your binary values, select an operation, and get instant results in binary, decimal, and hexadecimal formats.

Binary Conversion Table

Understanding how binary numbers correspond to decimal numbers is fundamental to working with binary calculations. Here's a quick reference table:

For easy conversions between different number systems, check out our other tools like Binary Translator for text-to-binary conversion.

Binary Addition Calculator

There is a similarity between the addition process used in the binary system and the process of addition used in the decimal system. When there is a need to carry more than 1, then the values added become equal to 10 (in binary), which happens when the addition equals 2 in decimal. The binary addition rules are simple:

Example: Let's add 1011 (11 in decimal) + 1101 (13 in decimal)

    1 1 1    (carries)
    1 0 1 1
  + 1 1 0 1
  ---------
  1 1 0 0 0  = 24 in decimal

Our binary addition calculator handles all carrying automatically, making it simple to add binary values without manual methods. Just enter your binary numbers and click Calculate!

Binary Subtraction Calculator

Binary subtraction is similar to decimal subtraction, but it uses only 0 and 1. The concept of borrowing happens when the number being subtracted is greater than the number from which it is being subtracted. In the binary system, borrowing becomes necessary when subtracting 1 from 0.

Example: Let's subtract 1010 (10 in decimal) - 0110 (6 in decimal)

    1 0 1 0
  - 0 1 1 0
  ---------
    0 1 0 0  = 4 in decimal

Use our binary subtraction calculator to perform subtractions instantly without worrying about borrowing rules—we handle all the complexity for you.

Binary Multiplication Calculator

The process of binary multiplication is actually easier than decimal multiplication because only the digits 0 and 1 are used. The multiplication rules are straightforward: anything multiplied by 0 equals 0, and anything multiplied by 1 equals itself. The challenge comes from aligning and adding the partial products.

Example: Let's multiply 101 (5 in decimal) × 11 (3 in decimal)

      1 0 1
    ×     1 1
    ---------
      1 0 1    (101 × 1)
    1 0 1      (101 × 1, shifted left)
    ---------
    1 1 1 1    = 15 in decimal

Our binary multiplication calculator handles all shifting and addition of partial products automatically, giving you accurate results in seconds.

Binary Division Calculator

The concept of division in the binary system is the same as in the decimal system. The divisor divides the dividend, but instead of decimal subtraction, we use binary subtraction. Binary division requires skill in binary subtraction to perform accurately.

Example: Let's divide 1100 (12 in decimal) ÷ 11 (3 in decimal)

        1 0 0  (quotient)
      --------
  11 | 1 1 0 0
       1 1
       -----
         0 0 0
           0 0
         -----
           0 0  (remainder)
           
Result: 100 (4 in decimal)

Use our binary division calculator to divide binary numbers effortlessly. The tool performs all subtraction steps and provides the quotient in binary, decimal, and hexadecimal formats.

How to Use Our Binary Calculator

Using ProURLMonitor's free binary calculator is incredibly simple. Follow these steps to perform binary calculations:

1. Enter First Number: Type your first binary number in the "First Number" field. Only use digits 0 and 1.
2. Select Operation: Choose your desired operation from the dropdown menu:
   • Add (+) for addition
   • Subtract (-) for subtraction
   • Multiply (×) for multiplication
   • Divide (÷) for division
3. Enter Second Number: Type your second binary number in the "Second Number" field.
4. Calculate: Click the green "Calculate" button to perform the operation.
5. View Results: See your results displayed in three formats:
   • Binary result - Answer in binary format
   • Decimal result - Answer converted to decimal
   • Hex result - Answer converted to hexadecimal
6. Reset: Click "Reset" to clear all fields and start a new calculation.

The calculator automatically validates your input to ensure only valid binary numbers (containing only 0 and 1) are processed. If you enter invalid characters, you'll receive an error message prompting you to correct your input.

Benefits of Using an Online Binary Calculator

Our online binary calculator offers numerous advantages for students, programmers, and digital electronics enthusiasts:

For text-based binary operations, you can also try our Binary Translator tool to convert text to binary and vice versa.

Related Binary Conversion Tools

ProURLMonitor offers a complete suite of number system conversion tools to complement our binary calculator: