The binary number system plays a significantly influential role in the computer age. The Binary number of the base is equal to 2, which indicates that it presents two numeric symbols in **binary calculator** such as 0 and 1.Gottfried Wilhelm Leibniz is the most famous mathematician, who is invented the binary number system in the 17th century. In the past era, it had been solving in an old calculating machine. Now, in recent days, the binary number is used by the two base numbers, where each position takes place in a **binary calculator** as a 1 and 0. In the modern world, multiplication, division, addition, and subtraction are estimated by the **binary calculator** within a second, same rule as applied in the decimal system. It uses as an engine of the mathematical or **binary calculator**. First, enter the equation with instantly get the result in the **binary calculator**.

## How to Construct the Binary

**Calculator** Number System:

The binary number system has eight characters in length, whereas each number is either a zero or one. Calculate the binary is a little bit difficult until you have to examine the system. Most of the time, we heard in the academic years that is the binary number uses base 10 or 2. In the support 2, you will have to apply the digit either 1 or 0, but alternately. Additionally, the counting starts from 0 to 9 under the base of 10 to calculate the overall value of binary numbers. Now, let’s start the example from the positive integer decimal number that is two hundred and thirty-five. For instance

(2× 10^{2}) + (3 × 10^{1}) + (5 × 10^{0})

200 + 30 + 5 = 235

We readout from the rightmost number multiplies by 100, then the next number multiply by 101, and so on. The subscript of the decimal number 10 represents the digit as a base 10 number.

**How to Add Two Binary Numbers**

The binary addition method is more familiar with the decimal addition, but there is one common difference between binary and decimal addition. Binary addition carries a value two, but the decimal system is equivalent to 10.

Four rules of binary addition

We remember to four states in binary addition before applying through the operation of addition. These are:

- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10

In fourth rules, the binary addition creates a sum is 10 – it can be written 0 digits in the given below column and the carry of one over from the last column to the right. Now, we discuss some examples for understanding the binary addition method.

Binary addition example:

^{1}0 | ^{1}1 | ^{1}1 | 1 | ||

+ | 1 | 1 | 1 | 1 | |

= | 1 | 0 | 1 | 1 | 0 |

The binary addition example gives the sum is 1001012. This answer provides the 4-bit binary number system range. The calculation has complete by using the digit with five, six, and more bits, so the result would be considered correct that is 101102. But if the most critical part is discarded from the result, so the answer 01102 would be wrong or incorrect. In binary addition, you have to be careful while calculating or solving a sum.

**How to Subtract Binary Number**

Binary subtraction plays a significant part in the digital electronic and binary arithmetic system. Likewise, as binary addition, there is a little bit difference between decimal and binary subtraction except the digit 0 and 1. In the binary subtraction case, we borrow where the figure is subtracted if it is larger than the other number.

Four rules of binary subtraction:

Before preceding the binary subtraction operation, so first, we must be kept the four fundamental steps of the subtraction.

- 0 – 0 = 0
- 0 – 1 = 1 ( borrow the digit 1 from the next significant bit)
- 1 – 0 = 1
- 1 – 1 = 0

Example of the binary subtraction

^{-1}1 | ^{2}0 | 1 | 1 | 1 | ||

– | 0 | 1 | 1 | 0 | 0 | |

= | 0 | 1 | 0 | 1 | 1 |

When one subtracts from 0, so the borrowing is essential for solving the problem in the binary subtraction, in the subtraction case, the 0 essentially becomes 2 ( 0-1 is change into 2-1, which equal to the one) in the borrowing column.

**How to Multiply Binary Number**

Binary multiplication is one of the most natural methods in the binary arithmetic operation. There is a fundamental correlation between the two digits, that is 0 and 1 during the multiplication process. Binary multiplication is the same as the decimal multiplication. The complexity arises from laborious binary addition, and it is based on how many binary bits present in each term

Four easy rules of the binary multiplication

There are four fundamental steps to be applied while doing a bigger or complex multiplication question. These are

- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1

In the fourth rule of multiplication, there is no need to borrow or carry for solving the problem.

Example of the binary multiplication

1 | 0 | 1 | 1 | 1 | |||

× | 1 | 1 | |||||

1 | 0 | 1 | 1 | 1 | |||

+ | 1 | 0 | 1 | 1 | 1 | 0 | |

= | 1 | 0 | 0 | 0 | 1 | 0 | 1 |

We can see in the above example, 0 placeholders are mention in the second line of multiplication, which is not present virtually in the decimal multiplication. If we do not use the 0 so it can be possible to make some mistakes while adding the binary numbers in the last step. But, the right 0 from the one is relevant or cannot exclude in the multiplication operation.

**How to Divide Two Binary Numbers**

The binary division is the most significant part of the binary arithmetic, but it is a little bit complex than the other binary operations. This multiplication process is the same as the decimal division, but the overall procedure of the binary division is quite a long division method. Subtraction is the critical phenomenon for binary division, before calculating the binary division method, so first, we have to understand the binary subtraction. There has the same rule applies the same as already explained in the above part.

Example of the binary division

101)11010(101->quotient

101

___________________________

00110

101

____________________________

001-> remainder

In the first step, we divide by the leftmost number of dividends then again share until the operation of division has complete. In the last, the binary division result obtained 101 quotients, and the remainder is 001 in the bottom.

**How to Convert Binary Into Decimal Number**

The binary number system can be converted into a decimal number, which means that the base of 2 changed into the bottom of 10. Nowadays, it can easily convert by a single click of the binary calculator for examining the binary number system.

There are four easy steps of the conversion of binary into a decimal number. It includes multiplying the value of every name such as 1 or 0 by the digit of the place holder of the number.

- first, we write down the given values
- begin with the least significant bit (LSB)
- multiply the cost by the number of the place holder
- then continue doing the process until you have to reach the most significant bit
- Last, combine the result at a one place

**Binary To Decimal Conversion Table**

Binary | Decimal |

0 | 0 |

1 | 1 |

10 | 2 |

11 | 3 |

100 | 4 |

101 | 5 |

110 | 6 |

111 | 7 |

The binary number system value of 0 remains 0 after the conversion into a decimal number. The third conversion value of the binary value 11 changed into the three decimal form, and in the last given binary value, 111 is 7, and the process goes on because we have already discussed in the above description that the binary number system of the base is 2 and the decimal number system of the support is 10.

**Conversion a Decimal Number system to a Binary Number system:**

Converting a decimal number system into the binary number system is the reverse process of the prior method. It includes each value repeatedly dividing by the decimal number 2 until the end of the given value.

There are three easy steps of the decimal number value into a binary number value.

- First, we write the decimal number and divide it by two continually until we have to obtain the final answer. The result can be either 0 or 1.
- If the quotient of the decimal number is zero so that you have complete the overall process
- Otherwise, we will have to move toward on step 1, then multiply by the most recent quotient value from level 1 to step 3.

Example of the decimal into binary conversion system

** ****Binary/Decimal Conversion**

Decimal | Binary |

0 | 0 |

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

7 | 111 |

8 | 1000 |

10 | 1010 |

16 | 10000 |

20 | 10100 |

In the above example, the decimal value of the one always remains one, and the four-digit decimal number is 100. The same process must be continuing for any required decimal number. Every step of the decimal and binary numbers system is straightforward if you must follow every step carefully.