The decimal and binary number systems are the world’s most commonly used number systems right now.

The decimal system, also known as the base-10 system, is the system we utilize in our everyday lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. On the other hand, the binary system, also known as the base-2 system, utilizes only two digits (0 and 1) to represent numbers.

Comprehending how to convert between the decimal and binary systems are vital for many reasons. For instance, computers use the binary system to portray data, so software engineers must be competent in converting among the two systems.

Furthermore, understanding how to change among the two systems can helpful to solve math questions including enormous numbers.

This blog will go through the formula for transforming decimal to binary, provide a conversion table, and give instances of decimal to binary conversion.

## Formula for Changing Decimal to Binary

The method of changing a decimal number to a binary number is done manually using the ensuing steps:

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

Divide the quotient (only) collect in the previous step by 2, and record the quotient and the remainder.

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

The binary equal of the decimal number is acquired by inverting the sequence of the remainders obtained in the last steps.

This might sound complex, so here is an example to illustrate 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 inverting the sequence of remainders (1, 0, 0, 1, 0, 1, 1).

## Conversion Table

Here is a conversion chart showing the decimal and binary equivalents 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 instances of decimal to binary transformation using the steps talked about priorly:

Example 1: Convert 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, which is gained by reversing the series of remainders (1, 1, 0, 0, 1).

Example 2: Convert 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 achieved by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).

While the steps described above offers a way to manually convert decimal to binary, it can be labor-intensive and error-prone for large numbers. Thankfully, other methods can be employed to rapidly and effortlessly convert decimals to binary.

For instance, you can use the incorporated functions in a calculator or a spreadsheet application to convert decimals to binary. You could further utilize online applications for instance binary converters, that allow you to input a decimal number, and the converter will spontaneously produce the respective binary number.

It is worth pointing out that the binary system has some limitations compared to the decimal system.

For instance, the binary system cannot represent fractions, so it is solely appropriate for dealing with whole numbers.

The binary system additionally needs more digits to illustrate a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, that has six digits. The length string of 0s and 1s can be prone to typos and reading errors.

## Concluding Thoughts on Decimal to Binary

In spite of these limits, the binary system has a lot of merits with the decimal system. For instance, the binary system is lot easier than the decimal system, as it just uses two digits. This simplicity makes it easier to carry out mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.

The binary system is further suited to representing information in digital systems, such as computers, as it can easily be depicted using electrical signals. Consequently, understanding how to convert between the decimal and binary systems is essential for computer programmers and for unraveling mathematical problems including large numbers.

Although the process of converting decimal to binary can be time-consuming and prone with error when done manually, there are tools which can easily change within the two systems.