Binary Calculator

A binary calculator is a tool that is used to estimate binary digits or numbers. The binary calculator is used for the addition of binary numbers, for the subtraction of binary numbers, multiplication, and we can also divide binary numbers very easily. A binary calculator contains a total of eleven operations which is capable of performing the logic operations on the given numbers or digits. A binary calculator provides the results in binary, decimal, and hex numbers.

We know that according to the concepts of digital electronics and mathematics, a binary number is a number expressed in terms of the base-2 number system which is also known as the binary number system. The binary number system comprises of only two digits that include: “0” (Zero or off state) and “1” (one or on-state). The binary number system (or the base-2 number system) is said to be a positional notation with a radix of 2. Furthermore, every digit is known as a bit of a binary digit.

When we say a binary number, we need to refer to each digit, for example, the binary number “1112” is simply expressed as “one one one two”. Once we exactly know about the binary term, we don’t get confused with the decimal number. Every individual binary digit (such as “0” or “1”) will be called a “bit”. For example, 1110101 is seven bits long.

Binary Addition Calculator

The binary number system is one of the numerical systems that works identical to the decimal number system that which is most widely used by everyone. The decimal number system is explained by the number 10 i.e., the decimal number system includes digits 0 to 9 for counting. In other words, a decimal system is a base 10 number system, whereas the binary number system is a base 2 number system.

In the binary number systems we use only 0 and 1, these are known as “bits” or “binary digits. All the algebraic operations such as addition, multiplication, subtraction, and division, apart from these variations, are measured according to the same principles as the decimal system.

The addition of binary numbers obeys the same rule as in the decimal addition, but it generally carries 1 instead of 10. The binary calculator executes the adding rules for the addition of binary digits. 

Electronic equipment that performs the binary addition is popularly known as a binary adder in digital electronics & communications and in general binary addition calculators. Any arithmetic and algebraic operation in digital circuits takes place in the binary form, thus, the Binary addition is one of the most fundamental & vital arithmetic operations to process the instruction.

Let us have a look at an example for binary addition:

\[\Rightarrow\] \[1 + 0\] = \[1\]

\[\Rightarrow\] \[0 + 1\] = \[0\], and carry 1 to the next more significant bit

Binary Subtraction Calculator With Steps

Similar to the binary addition, the binary subtraction of binary numbers is almost the same, excluding those emerging from the use of only numbers 0 and 1. If the amount withdrawn is greater than the number withdrawn, the number will always be borrowed.

In binary subtraction, borrowing only makes sense if 1 is subtracted from 0. In this case, 0 in the "Borrow" column becomes 2, and  1 in the "Borrow" column decreases. If the next column is also  0, then each column must be subsequently borrowed to reduce the columns with values ​​1 to 0.

Let us now have a look at the binary subtraction examples:

\[\Rightarrow\] \[1 - 0\] = \[1\]

\[\Rightarrow\] \[0 - 1\] = \[1\] ( with a borrow of 1)

Electronic equipment that performs binary subtraction is popularly known as a binary subtractor in digital electronics & communications. In general, binary subtraction calculators are used to performing the calculations. 

Binary Multiplication

Like binary addition and subtraction, binary multiplication is not as complicated as it looks. The only values ​​used are 0 and 1, so the number you add is the same as the first word or 0. Note that you need to insert placeholder 0 in each subsequent section and shift the value to the left, similar to 10 base multiplication. 

For example:

\[\Rightarrow\] \[1 \times 0\] = \[0\]

\[\Rightarrow\] \[1 \times 1\] = \[1\] (No borrow or carry method is applicable here)

Binary multiplication may seem a bit tricky, as it repeats binary additions, but it's not that hard. The binary process is the same as decimal multiplication, as shown in the example. Notice that the placeholder on the second line is 0. The zero placeholders for decimal multiplication is usually not physically visible. We can do perform all these multiplication operations on a binary multiplication calculator for quick calculations.

If 0 is not specified, you can make the mistake of excluding 0 when applying the above binary values. Remember again that in a binary system, the 0 to the right of the 1 is important, but the 0 to the left of the last 1 is not important in that sense.

Binary Division

The binary division process is similar to the tedious decimal system division. The dividends are always evenly separated by the divisor. The only major difference is the use of binary numbers instead of decimal subtraction. It is important to understand the binary subtraction of binary division. Let's use an example to understand binary division.

\[\Rightarrow\] \[1 \div 1\] = \[1\]

\[\Rightarrow\] \[0 \div 1\] = \[0\]

\[\Rightarrow\] \[1 \div 0\] = \[0 \div 0\] = meaningless

Further, a binary division calculator can be used for performing seamless calculations.

Conversion of Binary Numbers to Decimal

The conversion of binary to decimal conversion can be done in the easiest way by adding the products of each binary digit with its weight (It will be in the form of binary digit × 2 raised to a power of the position of the digit) starting from the right-most digit which has a weight of  \[2^{0}\].

Binary to decimal conversion is usually done by using two methods as listed below: 

• The positional notation method

• Doubling method. 

Most widely used is the positional notation method for converting binary to decimal.

In binary, 8 is considered as 1000. If we read from right to left, the 1 represents 23, the first 0 represents 22, the second 0 represents 21, and the 0 at the left represents 20. The only difference between decimal and binary systems is having a base of 2 instead of 10, rest is just similar to the decimal system. 

Let us have a look at the following conversion example;

\[(11001)_{2}\] =  \[(\textrm{1}\] \[\times\] \[2^{4})\] + \[(\textrm{1}\] \[\times\] \[2^{3})\] + \[(\textrm{0}\] \[\times\] \[2^{2})\] + \[(\textrm{0}\] \[\times\] \[2^{1})\] + \[(\textrm{1}\] \[\times\] \[2^{0})\]   = \[\textrm{16 + 1 + 0 + 0 + 1}\] = \[(18)_{10}\]

Binary to Decimal Conversion

Similarly, we can do decimal to binary conversion just like binary to decimal conversion. Now let us have a look at an example for the conversion.

For converting a decimal number to binary we divide the given decimal number by 2 till we get 0 as quotient. The first remainder obtained by dividing the given number by 2 will least significant digit and it will be placed on the rightmost. The last remainder obtained will be the most significant digit and this will be placed on the leftmost. Let us convert 21 to binary digits:

Therefore from the above calculation, we found that (21)10 decimal number binary equivalent is (10101)2. 

It is easier to convert from binary to decimal. Determine all positions of 1 and calculate the sum of the values.

These are all the types of a binary arithmetic calculator, we can even find methods for binary addition converter with steps on this page.

Did You Know?

• We can easily convert the binary number to a decimal number (upto a count of 15) by using the “8421” method. 

• For example, consider the binary number 1101, now let us use “8421” method to convert it to a decimal number. Place the binary number as it is without changing the positions of 8421 and then find the sum of 1’s. 

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• By position method: \[(1101)_{2}\] = \[\textrm{1}\] \[\times\] \[2^{3}\] + \[\textrm{1}\] \[\times\] \[2^{2}\] + \[\textrm{0}\] \[\times\] \[2^{2}\] + \[\textrm{1}\] \[\times\] \[2^{0}\] = \[\textrm{8 + 4 + 0 + 1}\] = \[(13)_{10}\]