Using binary calculators, we can add, subtract, multiply or break two binary values, translate binary values into decimal values, and vice versa.

Binary Calculator

Binary Numbers System

The binary system is a numerical system that operates essentially the same as the system of decimal numbers that people are generally more familiar with. Although the number 10 is used by the decimal number system as its basis, 2 are used by the binary system.

Also, while the decimal system uses digits 0 through 9, only 0 and 1 are used by the binary system and each digit is referred to as a bit.

Other than these differences, all operations are computed according to the same rules as the decimal system, such as addition, subtraction, multiplication, and division.

Due to its ease of implementation in digital circuitry using logic gates, nearly all modern technology and computers use the binary system. Designing hardware that needs only to detect two states, on and off, is much simpler.

Binary Calculator

This is a binary calculator for arbitrary-precision. Two binary numbers may be added, subtracted, multiplied, or divided. It can work on very large integers and very tiny fractional values, and combinations of both.

This calculator, by design, is very easy. You can use it to explore, in its most basic form, binary numbers. It works on “pure” binary numbers, not formats of computer numbers like the complement of two or IEEE binary floating-point.

Use of Binary Calculator


  1. Enter each box with one operand. Each operand must be a positive or negative number, not represented as a percentage, and not in scientific notation, with no commas or spaces. A radix point (‘.’, not ‘,’) is used to indicate fractional values, and negative numbers are prefixed with a minus sign (‘-‘).
  2. Pick (+,-*,/) an activity.
  3. Adjust the number of bits that you want to show in the binary result, if the default is different (this applies only to division, and then only when the answer has an infinite fractional part).
  4. To execute the process, press ‘Calculate’.
  5. To reset the form, click ‘Clear’ and start from scratch.

Type over the original number and press ‘Calculate’ if you want to adjust an operand, there is no need to click ‘Clear’ first. Similarly, you can adjust the operator and retain the operands as they are.


The number of digits in the operands and the result are shown in addition to the output of the procedure. For instance, the “Num Digits” box shows “1.4 * 3.6 = 4.10” when calculating 1.1101 * 111.100011 = 1101.1010110111.

This means that in its integer part, operand 1 has one digit and in its fractional part four digits, in its integer part, operand 2 has three digits and in its fractional part six digits, and its integer part, the result has four digits and in its fractional part ten digits.

Addition, subtraction, and multiplication often produce a finite outcome, but the division will produce an infinite (repeating) fractional value (in fact, in most cases). Infinite results are truncated to the specified number of bits, not rounded.

With an ellipsis appended to the result, and with an ‘al’ symbol as the number of fractional digits, infinite outcomes are noted.

For divisions representing dyadic fractions, regardless of the setting for the number of fractional bits, the result will be finite and shown in full precision.

“For instance, 0.000110011001100110011001… is 1/1010 to 24 fractional bits, with “Num Digits” = “1.0 / 4.0 = 0. ⁇ “; 11/100 = 0.11, with “Num Digits” = “2.0 / 3.0 = 0.2”.

Use Of Binary Calculator

Solve Floating Numbers from Binary Calculator

While pure binary arithmetic is implemented by this calculator, you can use it to explore floating-point arithmetic. For e.g., say you wanted to know why 129.95 * 10 = 1299.5, but 129.95 * 100 = 12994.9999999999998181010596454143524169921875, using IEEE double-precision binary floating-point arithmetic.

In such a measurement, there are two sources of inaccuracy: decimal to floating-point conversion, and binary arithmetic of minimal precision.

Decimal to floating-point conversion creates inaccuracy because a decimal operand may not have an exact floating-point equivalent; binary arithmetic of limited precision creates inaccuracy because a binary calculation can generate more bits than can be stored.

Binary Addition

Binary addition operates in the same way as an addition in the decimal system, except that when the added values are equal to 10, carry over takes place when the addition result is equal to 2 instead of carrying a 1 over.

The only real distinction between the inclusion of binary and decimal is that in the binary system, the value 2 is equal to 10 in the decimal system. Note that the digits that are carried over reflect the superscripted 1s. In the case where 1 + 1 = 0 also has a 1 carried over from the previous column to its right, a common error to look out for when performing binary addition is?

Binary Addition Calculator

There is a comparison between the addition method used in the binary system and the addition procedure used in the decimal system. If there is a need for more than 1 to be transported, then the additional values are equal to 10, when the addition is equal to 2. To learn more about adding binary numbers, please see the equation below:


An easy way to add binary values without the use of manual methods is the binary addition calculator.

Binary Subtraction

There is no variation between binary and decimal subtraction, similar to binary addition, excluding those that occur from using only the digits 0 and 1. In any case, borrowing occurs where the number subtracted is greater than the number from which it is subtracted. The only case where borrowing is necessary for binary subtraction is when 1 is subtracted from 0.

“When this happens, the 0 in the borrowing column becomes effectively “2” (changing 0-1 into 2-1 = 1) thus reducing the 1 in the borrowing column by 1. If the following column is also 0, borrowing from each subsequent column must take place before a column with a value of 1 can be decreased to 0.

Binary Subtraction Calculator

There is a link between the binary system and the subtraction of the decimal system here as well. But, in the case of the use of 0 and 1, it is different. If the number deducted is greater than the number from which it is deducted, the principle of borrowing exists.

The condition where it is extremely necessary to borrow would occur in the subtraction phase of the binary system when the number 1 is deducted from 0. The number 0 in the borrowing column is changed to the number ‘2’ in this case. When subtracting the number 1 from the segment from which the number 1. is borrowed,

The other column also consists of the number 0, so borrowing from the next column will take place before we enter a column with a number 1 that can be deducted from the number 0.

An easy tool for subtracting binary values without using manual methods is the binary subtraction calculator.

Binary Subtraction calculator

Binary Multiplication

Arguably, binary multiplication is better than its decimal equivalent. Since 0 and 1 are the only values used, the results that have to be applied are either the same as the first word, or 0. Notice that it is appropriate to add placeholder 0’s in each subsequent row, and the value is moved to the left, just as in decimal multiplication.

Depending on how many bits are in each word, the difficulty of binary multiplication emerges from tedious binary addition.

Binary Multiplication Calculator

The method is simpler in the binary system than it is in the decimal system. Because only the numbers 0 and 1 are used, the result that is applied may be identical to the first word, or it may be 0.0. The number 0 is applied to all the following rows as a result of the value moving to the left, as occurs in the decimal multiplication process.

The trickiness in the binary process computations arises from monotonous calculations that in each term depend on the bits.

An easy tool for multiplying binary values without the use of manual methods is the binary multiplication calculator.

Binary Division

In the decimal system, the method of binary division is identical to long division. The dividend is also broken in the same way by the divider, with the use of binary rather than decimal subtraction being the only major difference. Notice that for conducting binary division, a good understanding of binary subtraction is necessary.

Binary Division Calculator

In the binary system, the concept of division is the same as the enormous processes of a decimal system involving division. The divider splits the dividend again, using the binary subtraction over here and not the decimal subtraction. You have to be proficient in binary deductions and subtraction, otherwise, it will be hard for you.

Frequently Asked Questions (FAQs)

How do you perform binary code calculations?

To calculate the numerical value of a binary number, add the value of all 1s in an eight-character number to each location. For instance, the number 01000001 is translated to 64 + 1 or 65.

How are you meant to say hello in binary?

In binary code, the term “hello” is: 011010000110010101101100011011000110111111 It is simpler to see the binary byte corresponding to each letter by splitting it into eight-digit segments: 01101000000110010101101101100 01101100 011011100 011011111-you may check that with the binary translator.

How can you describe the infant binary?

Using just two digits, the binary numeral method is a way of writing numbers: 0 and 1. These are used as a set of “off” and “on” switches in computers. In binary, the location value of each digit is twice as much as that of the next digit to the right (since each digit holds two values).


The binary calculator is the way knowledge, 1’s and 0’s, is kept by a machine. It was interesting, I thought, and that it would be worth studying. It is well worth learning, and learning is very easy.