Binary Calculator

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To use Binary Calculator, enter the values in the input boxes below and click on Calculate button.



A binary calculator is a tool or a program designed to perform arithmetic operations on binary numbers, which are numbers expressed in the base-2 numeral system. The binary system uses only two digits, 0 and 1, to represent numbers.

Here are the details of a binary calculator and how it works:

  1. Binary Representation: In a binary calculator, numbers are represented using the base-2 system. Each digit in a binary number is called a bit, where the rightmost bit represents the least significant bit (LSB), and the leftmost bit represents the most significant bit (MSB). For example, the binary number 1011 represents the decimal number 11.

  2. Arithmetic Operations: A binary calculator can perform basic arithmetic operations, such as addition, subtraction, multiplication, and division, on binary numbers.

    • Addition: Binary addition is similar to decimal addition. You add the corresponding bits, starting from the LSB and moving towards the MSB. If the sum of two bits is 0 or 1, it can be represented by a single bit. If the sum is 2, it is represented as 0 and a carry of 1. The carry is added to the next significant bit. For example:


      1101 (13 in binary)

    +1010 (10 in binary)

    10111 (23 in binary)



    - **Subtraction**: Binary subtraction is also similar to decimal subtraction. You subtract the corresponding bits, starting from the LSB and moving towards the MSB. If the minuend is smaller than the subtrahend, you need to borrow from the next significant bit. For example:

    1011 (11 in binary)

    • 110 (6 in binary)



    101 (5 in binary)



    - **Multiplication**: Binary multiplication is similar to decimal multiplication using the "multiplication by hand" method. You multiply the multiplicand with each bit of the multiplier, shifting the partial products to the left according to their positions. Then, you sum the partial products to get the final result. For example:



    1101 (13 in binary)

    x 1010 (10 in binary)

    11010 (26 in binary) 1101000




    - **Division**: Binary division is similar to decimal division using long division. You divide the dividend by the divisor, bit by bit, until the division is complete. The quotient is obtained by concatenating the remainders. For example:

    10111 (23 in binary) ÷ 101 (5 in binary)



    1 (Quotient: 1) 101



    111 (Remainder: 3 in binary)


  3. Conversion: Binary calculators often provide options to convert binary numbers to decimal numbers and vice versa. These conversions are useful when working with numbers in different numeral systems.

  4. User Interface: Binary calculators can have different user interfaces, ranging from simple command-line programs to graphical calculator applications. The interface typically includes input fields for entering binary numbers and buttons or options for selecting the desired arithmetic operation.

It's important to note that binary calculators can also handle larger numbers by using multiple bits, such as 8-bit, 16-bit, 32-bit, or even 64-bit representations. These calculators often include additional features like bitwise operations (AND, OR, XOR), left shift, right shift, and more, which are useful in