# How to Convert Decimal to Binary and Binary to Decimal

## The Binary Number System

The binary number system plays a major important 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 numbers system in the 17^{th} century. In the past era, it had been solved in an archaic calculating machine. Now, in recent days, the binary number is used by the 2 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 a binary numbers then instantly get the result in the binary calculator.

## How to Construct the Binary Number System:

The binary number system has eight characters in the length whereas each number is either a zero or one. Calculate the binary is 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 base 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 we 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 right most number multiplies by 10^{0}, then the next number multiply by 10^{1}, and so on. The subscript of the decimal number 10 represents the digit as a base 10 number.

**How to add two binary numbers**

Binary addition method is more familiar with the decimal addition, but there is a one common difference between binary and decimal addition. Binary addition carries a value 2 but the decimal system is equivalent to 10.

Four rules of binary addition

We remember to four rules 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 digit in the given below column and the carry of one over from a last column to right. Now, we discuss to some example 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 100101_{2}. This answer provides the 4-bit binary number system range. The calculation has been completed by using the digit with five, six, and more bits so the result would be considered correct that is 10110_{2}. But if the most important part is discarded from the result, so the answer 0110_{2 }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 a 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 digit 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 1 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 changed into 2-1 which equal to the one) in the borrowing column.

** How to Multiply Binary Number**

Binary multiplication is one of the easiest methods in the binary arithmetic operation. There is the fundamental correlation between the two digits that is 0 and 1 during the multiplication process. Binary multiplication is 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 placeholder is mentioned in the second line of multiplication which is not actually present virtually in the decimal multiplication. If, we does not use the 0 so it can be possible to make some mistake while adding the binary numbers in the last step. But, the right 0 from the 1 is relevant or cannot exclude in the multiplication operation.

** How to Divide Two Binary Numbers**

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

**Example of the Binary Division**

In the first step, we divide by the left most number of dividend then again divide until the operation of division has been completed. In the last, the binary division result obtained 101 quotient and the remainder is 001 in the bottom.