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

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 represent numbers. At the same time, the binary system, also called the base-2 system, employees only two digits (0 and 1) to represent numbers.

Understanding how to transform from and to the decimal and binary systems are essential for multiple reasons. For example, computers utilize the binary system to depict data, so computer programmers should be competent in converting between the two systems.

Additionally, comprehending how to change among the two systems can helpful to solve mathematical questions including large numbers.

This article will cover the formula for changing decimal to binary, offer a conversion table, and give examples of decimal to binary conversion.

## Formula for Converting Decimal to Binary

The method of transforming 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) collect in the prior step by 2, and record the quotient and the remainder.

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

The binary equivalent of the decimal number is achieved by reversing the order of the remainders obtained in the last steps.

This might sound confusing, so here is an example to portray 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 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 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 examples of decimal to binary conversion using the method talked about earlier:

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, that is obtained by reversing the sequence 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 equal of 128 is 10000000, that is obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).

While the steps described above provide a way to manually change decimal to binary, it can be tedious and error-prone for big numbers. Fortunately, other systems can be employed to swiftly and simply change decimals to binary.

For instance, you can utilize the incorporated features in a spreadsheet or a calculator application to convert decimals to binary. You can further use web-based tools similar to binary converters, which enables you to enter a decimal number, and the converter will spontaneously produce the equivalent binary number.

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

For example, the binary system cannot portray fractions, so it is solely 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 represented by the binary number 1100100, that has six digits. The long string of 0s and 1s can be inclined to typing errors and reading errors.

## Concluding Thoughts on Decimal to Binary

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

The binary system is more fitted to representing information in digital systems, such as computers, as it can easily be portrayed using electrical signals. As a result, knowledge of how to transform among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical questions concerning huge numbers.

Even though the process of converting decimal to binary can be labor-intensive and error-prone when worked on manually, there are tools which can easily convert among the two systems.