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December 16, 2022

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

The decimal system, also under the name of the base-10 system, is the system we use in our daily lives. It utilizes ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. On the other hand, the binary system, also called the base-2 system, employees only two digits (0 and 1) to depict numbers.

Learning how to convert between the decimal and binary systems are essential for various reasons. For instance, computers use the binary system to depict data, so computer engineers should be expert in converting between the two systems.

Furthermore, comprehending how to change between the two systems can helpful to solve mathematical problems concerning enormous numbers.

This blog article will cover the formula for transforming decimal to binary, give a conversion chart, and give examples of decimal to binary conversion.

## Formula for Changing Decimal to Binary

The procedure of changing a decimal number to a binary number is done manually utilizing the following steps:

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

2. Divide the quotient (only) found in the prior step by 2, and document the quotient and the remainder.

3. Repeat the prior steps until the quotient is equivalent to 0.

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

This might sound confusing, so here is an example to portray this method:

Let’s convert the decimal number 75 to binary.

1. 75 / 2 = 37 R 1

2. 37 / 2 = 18 R 1

3. 18 / 2 = 9 R 0

4. 9 / 2 = 4 R 1

5. 4 / 2 = 2 R 0

6. 2 / 2 = 1 R 0

7. 1 / 2 = 0 R 1

The binary equivalent of 75 is 1001011, which is obtained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).

## Conversion Table

Here is a conversion chart 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 few instances of decimal to binary transformation employing the steps discussed priorly:

Example 1: Convert the decimal number 25 to binary.

1. 25 / 2 = 12 R 1

2. 12 / 2 = 6 R 0

3. 6 / 2 = 3 R 0

4. 3 / 2 = 1 R 1

5. 1 / 2 = 0 R 1

The binary equal of 25 is 11001, that is acquired by inverting the sequence of remainders (1, 1, 0, 0, 1).

Example 2: Change the decimal number 128 to binary.

1. 128 / 2 = 64 R 0

2. 64 / 2 = 32 R 0

3. 32 / 2 = 16 R 0

4. 16 / 2 = 8 R 0

5. 8 / 2 = 4 R 0

6. 4 / 2 = 2 R 0

7. 2 / 2 = 1 R 0

1. 1 / 2 = 0 R 1

The binary equivalent of 128 is 10000000, which is obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).

Although the steps described prior offers a way to manually convert decimal to binary, it can be time-consuming and error-prone for large numbers. Luckily, other methods can be utilized to swiftly and simply convert decimals to binary.

For instance, you can employ the built-in features in a spreadsheet or a calculator application to change decimals to binary. You could further utilize online tools similar to binary converters, which allow you to input a decimal number, and the converter will automatically produce the respective binary number.

It is worth noting that the binary system has handful of constraints compared to the decimal system.

For instance, the binary system fails to represent fractions, so it is solely suitable 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 portrayed by the binary number 1100100, that has six digits. The extended string of 0s and 1s can be inclined to typing errors and reading errors.

## Final Thoughts on Decimal to Binary

Despite these restrictions, the binary system has some merits over the decimal system. For example, the binary system is lot easier than the decimal system, as it just utilizes 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 represented utilizing electrical signals. As a consequence, knowledge of how to transform between the decimal and binary systems is important for computer programmers and for unraveling mathematical problems concerning large numbers.

Even though the process of changing decimal to binary can be tedious and prone with error when worked on manually, there are applications that can easily change within the two systems.