 We Tutor All Subjects & Grade Levels - In Home And Online
December 16, 2022

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

The decimal system, also known as the base-10 system, is the system we use in our daily lives. It uses 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 figures (0 and 1) to portray numbers.

Learning how to transform from and to the decimal and binary systems are essential for many reasons. For instance, computers use the binary system to portray data, so software programmers must be proficient in converting among the two systems.

In addition, understanding how to change between the two systems can helpful to solve mathematical problems including enormous numbers.

This article will go through the formula for converting decimal to binary, give a conversion chart, and give instances of decimal to binary conversion.

## Formula for Converting Decimal to Binary

The method of transforming a decimal number to a binary number is performed manually using the ensuing steps:

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

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

3. Reiterate the previous steps unless the quotient is similar to 0.

4. The binary equivalent of the decimal number is obtained by inverting the order of the remainders obtained in the prior steps.

This may sound complex, so here is an example to show you this process:

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 equal 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 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 conversion utilizing the steps talked about 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 equivalent of 25 is 11001, that is obtained 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 achieved by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).

Although the steps outlined above provide a way to manually change decimal to binary, it can be labor-intensive and error-prone for big numbers. Thankfully, other systems can be utilized to quickly and simply convert decimals to binary.

For example, you could utilize the built-in functions in a calculator or a spreadsheet program to change decimals to binary. You could also use web tools such as binary converters, which allow you to input a decimal number, and the converter will spontaneously generate the corresponding binary number.

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

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

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

## Final Thoughts on Decimal to Binary

In spite of these limitations, the binary system has a lot of advantages with the decimal system. For example, the binary system is lot easier than the decimal system, as it just uses two digits. This simplicity makes it simpler to perform mathematical operations 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 simply be portrayed using electrical signals. As a result, understanding how to convert between the decimal and binary systems is essential for computer programmers and for solving mathematical questions involving huge numbers.

Although the method of changing decimal to binary can be labor-intensive and prone with error when done manually, there are tools that can easily convert between the two systems.   