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

The decimal system, also under the name of the base-10 system, is the system we use in our everyday lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. However, the binary system, also called the base-2 system, uses only two figures (0 and 1) to represent numbers.

Comprehending how to convert between the decimal and binary systems are important for various reasons. For instance, computers use the binary system to depict data, so computer programmers are supposed to be expert in converting within the two systems.

Furthermore, understanding how to change within the two systems can be beneficial to solve mathematical problems including enormous numbers.

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

## Formula for Converting Decimal to Binary

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

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

Divide the quotient (only) obtained in the previous step by 2, and document the quotient and the remainder.

Reiterate the prior steps unless the quotient is equal to 0.

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

This may sound confusing, so here is an example to show you this method:

Let’s change 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 equivalent of 75 is 1001011, which is acquired 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 some examples of decimal to binary conversion utilizing the method talked about 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 equivalent of 25 is 11001, which is gained by inverting the sequence 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, which is acquired by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).

While the steps defined prior offers a method to manually convert decimal to binary, it can be labor-intensive and open to error for big numbers. Thankfully, other systems can be employed to swiftly and simply change decimals to binary.

For instance, you can employ the incorporated features in a spreadsheet or a calculator application to change decimals to binary. You could further use web tools such as binary converters, which enables you to input a decimal number, and the converter will spontaneously produce the corresponding binary number.

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

For example, the binary system cannot portray fractions, so it is only fit for representing whole numbers.

The binary system further requires more digits to illustrate a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, that has six digits. The long string of 0s and 1s could be prone to typing errors and reading errors.

## Concluding Thoughts on Decimal to Binary

Despite these limits, the binary system has several merits over the decimal system. For instance, the binary system is lot easier than the decimal system, as it just utilizes two digits. This simplicity makes it easier to conduct mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.

The binary system is further fitted to depict information in digital systems, such as computers, as it can easily be represented using electrical signals. As a consequence, knowledge of how to change between the decimal and binary systems is crucial for computer programmers and for solving mathematical problems including large numbers.

While the method of changing decimal to binary can be time-consuming and prone with error when worked on manually, there are tools that can quickly change between the two systems.