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

The decimal system, also called the base-10 system, is the system we use in our everyday lives. It employees ten figures (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, uses only two figures (0 and 1) to represent numbers.

Comprehending how to transform from and to the decimal and binary systems are essential for multiple reasons. For instance, computers use the binary system to depict data, so computer programmers must be competent in converting between the two systems.

Additionally, comprehending how to convert within the two systems can help solve math problems concerning large numbers.

This blog will go through the formula for changing decimal to binary, provide a conversion table, 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 done manually utilizing the following steps:

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

Divide the quotient (only) found in the previous step by 2, and note the quotient and the remainder.

Replicate the last steps until the quotient is equal to 0.

The binary equivalent of the decimal number is acquired by reversing the series of the remainders obtained in the prior steps.

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

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 acquired by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).

## Conversion Table

Here is a conversion table portraying 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 some instances of decimal to binary conversion using the steps discussed 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, which is obtained by reversing 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, which is acquired by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).

Even though the steps defined earlier offers a method to manually change decimal to binary, it can be tedious and error-prone for big numbers. Luckily, other ways can be employed to swiftly and effortlessly convert decimals to binary.

For instance, you could use the built-in features in a calculator or a spreadsheet program to convert decimals to binary. You can further utilize online applications similar to binary converters, which allow you to input a decimal number, and the converter will automatically generate the equivalent binary number.

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

For example, the binary system is unable to illustrate fractions, so it is solely fit for dealing with whole numbers.

The binary system also requires more digits to represent a number than the decimal system. For instance, the decimal number 100 can be portrayed by the binary number 1100100, that has six digits. The extended string of 0s and 1s can be inclined to typos and reading errors.

## Last Thoughts on Decimal to Binary

In spite of these restrictions, the binary system has several advantages over the decimal system. For instance, the binary system is lot easier than the decimal system, as it only utilizes two digits. This simpleness makes it simpler to carry out mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.

The binary system is further fitted to representing information in digital systems, such as computers, as it can easily be represented using electrical signals. As a consequence, understanding how to transform among the decimal and binary systems is crucial for computer programmers and for solving mathematical problems involving huge numbers.

Although the process of changing decimal to binary can be labor-intensive and vulnerable to errors when worked on manually, there are applications that can quickly change between the two systems.