Related Calculators

The supports arbitrary precision and can add, subtract, multiply, or divide binary numbers. It is capable of computing large integers as well as very small fractional numbers. A very simple calculator that lets you explore binary numbers in their simplest form. It works with second-order binary numbers rather than two's complement numbers, IEEE binary floating-point numbers, or other computer number formats.

Binary numbers: what are they?

In binary numbers, all possible numerical values are represented by just two symbols: 0 and 1, based on the binary system, a positional numeral system with a base of two. For example, ten in decimal equals ten10 in binary, 100 in decimal equals one hundred in binary, and 1,000 in decimal equals one hundred thousand in binary. The binary system has signed, just as the decimal system does.

In the past, binary numerals were used by Egypt, China, India, and other countries. However, since the early 20th century, they have become mainly used by computer system designers, software engineers, programmers, and other computer system users. In a computer system, everything is represented by a one and a zero since the underlying system encodes everything with an electrical charge. In computer programming, a calculator or converter often comes in handy, and we do not need to compute in binary or do any arithmetic. Binary calculators are used for arithmetic operations (adding, subtracting, multiplying, and dividing binary numbers) and as binary converters for converting binary numbers to decimal, decimal numbers to binary, and binary numbers to hex.

Conversion from and to binary numbers

Performing a binary conversion to convert numbers to or from binary is unnecessary, as it only changes their form. Our binary converter above lets you convert both types of numbers quickly and easily, or below, you can read about how to perform a binary conversion manually. Binary conversion and calculation are separate operations: they do not have to be performed to be done.

  • Binary to decimal: Binary numbers represent powers of 2 in the same manner that decimal numbers represent powers of 10. It is, therefore, necessary to multiply each binary position number by two times the power of the position number to convert it to decimal, starting at zero and counting from right to left.

  • Decimal to Binary: It is more complex since we are switching from a higher base to a lower one. This is where you will appreciate having a binary converter handy. In this example, let us assume the decimal number X is to be converted to binary. To begin, determine how many times the power of 16 is multiplied by X, and denote it by E. Next, determine how many times this power of 16 has been multiplied by X. The remaining number will be Y1. You will then have your hex value by repeating the above steps. Start by assigning Yn to the 20 positions, then use the Yn value to multiply by two until it is greater than the remaining value. The remaining value should be assigned to the 21 positions.

Short notes on Binary Calculator

A binary calculator is a useful tool for performing arithmetic operations such as addition, subtraction, multiplication, division, and working with binary numbers. It can handle large binary numbers and provide results in binary and decimal formats. Here's how to use a binary calculator effectively:

Binary Addition:

Binary addition is similar to adding decimal numbers. Follow these rules:

- 0 + 0 = 0

- 0 + 1 = 1

- 1 + 0 = 1

- 1 + 1 = 0 (carry 1 to the next bit)

 To use the binary addition calculator:

  1. Enter the first binary number in the appropriate field.
  2. Enter the second binary number in the next field.
  3. The calculator will display the result of the addition in binary and decimal formats.

 Binary Subtraction:

Binary subtraction can be done using the borrow method or the complement method. The borrow method is similar to subtracting decimal numbers. The rules are:

- 0 - 0 = 0

- 0 - 1 = 1 (borrow one from the next bit)

- 1 - 0 = 1

- 1 - 1 = 0

To use the binary subtraction calculator:

  1. Enter the larger binary number first, and the smaller number second.
  2. Reverse the order of subtraction and add a minus sign at the end to find the result.
  3. The calculator will display the result of the subtraction in binary and decimal formats.

 Binary Multiplication:

Binary multiplication is similar to long multiplication with decimal numbers. The rules are:

- 0 * 0 = 0

- 0 * 1 = 0

- 1 * 0 = 0

- 1 * 1 = 1

 To use the binary multiplication calculator:

  1. Select the number of bits for your factors and products.
  2. Enter the binary factors in any order.
  3. The calculator will display the result of the multiplication in binary and decimal formats.

 Binary Division:

Binary division involves using binary multiplication and subtraction steps. It follows a process similar to long division with decimal numbers.

To use the binary division calculator:

  1. Enter the dividend and divisor in binary form.
  2. The calculator will display the quotient and remainder in binary and decimal formats

Binary Fractions:

Binary fractions represent fractional values using binary digits. Each digit to the right of the binary point represents a negative power of two.

 To use the binary fraction converter:

    1. Choose the conversion method (decimal to binary fraction or binary fraction to decimal).
    2. Enter the number of digits needed in the representation.
    3. The converter will provide the converted result.

Bit Shift Calculator:

A bit shift calculator performs logical shifts by moving binary digits to the left or right. It can be useful for various bitwise operations.

 To use the bit shift calculator:

      1. Choose the number of bits for the binary representation.
      2. Select the data type for your input.
      3. Enter the binary number.
      4. Select the direction of the shift (left or right).
      5. The calculator will display the shifted binary number in decimal, binary, and octal formats.

For precise calculations, please ensure that you input the binary numbers accurately and take into account their representation, including the sign.