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

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

Comprehending how to transform from and to the decimal and binary systems are vital for many reasons. For example, computers utilize the binary system to portray data, so computer programmers are supposed to be expert in converting among the two systems.

Additionally, understanding how to change between the two systems can be beneficial to solve math problems involving large numbers.

This blog will cover the formula for converting decimal to binary, provide a conversion table, and give examples of decimal to binary conversion.

## Formula for Changing 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 note the quotient and the remainder.

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

Replicate the prior steps before the quotient is similar to 0.

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

This might sound complex, so here is an example to portray 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 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 instances of decimal to binary transformation employing the steps 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, which is acquired 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 equal of 128 is 10000000, that is obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).

Although the steps outlined earlier provide a method to manually convert decimal to binary, it can be time-consuming and prone to error for large numbers. Fortunately, other methods can be employed to rapidly and effortlessly change decimals to binary.

For instance, you could use the built-in functions in a spreadsheet or a calculator application to convert decimals to binary. You can additionally use web-based tools for instance binary converters, that allow you to type a decimal number, and the converter will automatically generate the respective binary number.

It is worth noting that the binary system has some constraints contrast to the decimal system.

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

The binary system additionally needs more digits to portray 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 extended string of 0s and 1s can be inclined to typos and reading errors.

## Concluding Thoughts on Decimal to Binary

In spite of these limits, the binary system has some merits with the decimal system. For instance, the binary system is far simpler than the decimal system, as it just uses two digits. This simplicity makes it simpler to carry out mathematical functions in the binary system, for instance 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 represented utilizing electrical signals. Consequently, knowledge of how to convert among the decimal and binary systems is important for computer programmers and for solving mathematical questions including huge numbers.

Even though the process of changing decimal to binary can be tedious and error-prone when done manually, there are tools that can rapidly change within the two systems.