The decimal and binary number systems are the world’s most frequently used number systems presently.

The decimal system, also known as the base-10 system, is the system we use in our daily lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. At the same time, the binary system, also called the base-2 system, employees only two figures (0 and 1) to portray numbers.

Comprehending how to convert between the decimal and binary systems are important for multiple reasons. For instance, computers utilize the binary system to depict data, so computer engineers must be competent in changing within the two systems.

In addition, understanding how to change within the two systems can help solve math problems including large numbers.

This article will cover the formula for changing decimal to binary, provide a conversion chart, and give instances of decimal to binary conversion.

## Formula for Changing Decimal to Binary

The procedure of converting a decimal number to a binary number is done manually using the ensuing steps:

Divide the decimal number by 2, and account the quotient and the remainder.

Divide the quotient (only) found in the last step by 2, and record the quotient and the remainder.

Replicate the previous steps before the quotient is equal to 0.

The binary corresponding of the decimal number is acquired by reversing the order of the remainders acquired in the last steps.

This might sound complex, so here is an example to show you this process:

Let’s convert the decimal number 75 to binary.

75 / 2 = 37 R 1

37 / 2 = 18 R 1

18 / 2 = 9 R 0

9 / 2 = 4 R 1

4 / 2 = 2 R 0

2 / 2 = 1 R 0

1 / 2 = 0 R 1

The binary equal of 75 is 1001011, which is gained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).

## Conversion Table

Here is a conversion table depicting the decimal and binary equals of common numbers:

Decimal | Binary |

0 | 0 |

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

## Examples of Decimal to Binary Conversion

Here are few examples of decimal to binary conversion using the method discussed priorly:

Example 1: Change the decimal number 25 to binary.

25 / 2 = 12 R 1

12 / 2 = 6 R 0

6 / 2 = 3 R 0

3 / 2 = 1 R 1

1 / 2 = 0 R 1

The binary equal of 25 is 11001, that is acquired by inverting the series of remainders (1, 1, 0, 0, 1).

Example 2: Change the decimal number 128 to binary.

128 / 2 = 64 R 0

64 / 2 = 32 R 0

32 / 2 = 16 R 0

16 / 2 = 8 R 0

8 / 2 = 4 R 0

4 / 2 = 2 R 0

2 / 2 = 1 R 0

1 / 2 = 0 R 1

The binary equivalent of 128 is 10000000, that is obtained by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).

Although the steps described earlier offers a method to manually change decimal to binary, it can be time-consuming and open to error for large numbers. Fortunately, other ways can be used to quickly and effortlessly change decimals to binary.

For example, you could utilize the built-in features in a spreadsheet or a calculator application to convert decimals to binary. You could additionally use web applications such as binary converters, which enables you to type a decimal number, and the converter will spontaneously generate the respective binary number.

It is worth pointing out that the binary system has handful of constraints compared to the decimal system.

For example, the binary system cannot represent fractions, so it is only suitable for dealing with whole numbers.

The binary system additionally requires more digits to represent a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The extended string of 0s and 1s could be prone to typos and reading errors.

## Final Thoughts on Decimal to Binary

Despite these restrictions, the binary system has some merits with the decimal system. For instance, the binary system is lot easier than the decimal system, as it just utilizes two digits. This simpleness makes it simpler to carry out mathematical operations in the binary system, for instance addition, subtraction, multiplication, and division.

The binary system is further fitted to representing information in digital systems, such as computers, as it can simply be portrayed utilizing electrical signals. Consequently, understanding how to convert among the decimal and binary systems is essential for computer programmers and for solving mathematical questions including huge numbers.

Even though the method of converting decimal to binary can be tedious and error-prone when worked on manually, there are tools which can easily change within the two systems.