The decimal and binary number systems are the world’s most commonly utilized number systems presently.
The decimal system, also under the name of the base-10 system, is the system we utilize in our everyday lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. However, the binary system, also known as the base-2 system, uses only two figures (0 and 1) to depict numbers.
Learning how to convert between the decimal and binary systems are important for multiple reasons. For instance, computers utilize the binary system to depict data, so software engineers should be competent in converting within the two systems.
Furthermore, understanding how to convert among the two systems can help solve math problems concerning large numbers.
This blog article will cover the formula for transforming decimal to binary, provide a conversion chart, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The method of changing a decimal number to a binary number is performed manually utilizing the ensuing steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) obtained in the prior step by 2, and document the quotient and the remainder.
Replicate the previous steps until the quotient is similar to 0.
The binary corresponding of the decimal number is obtained by reversing the order of the remainders received in the last steps.
This might sound confusing, so here is an example to illustrate this process:
Let’s convert 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 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 table showing 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 method discussed priorly:
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 gained 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 outlined above offers a method to manually change decimal to binary, it can be time-consuming and error-prone for big numbers. Fortunately, other methods can be used to quickly and effortlessly convert decimals to binary.
For example, you could employ the built-in functions in a spreadsheet or a calculator program to convert decimals to binary. You can further use online tools for instance binary converters, which enables 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 in comparison to the decimal system.
For example, the binary system cannot represent fractions, so it is solely appropriate for dealing with whole numbers.
The binary system also requires more digits to portray 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 some advantages with the decimal system. For example, the binary system is much simpler than the decimal system, as it only utilizes two digits. This simpleness makes it easier to conduct mathematical operations in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is more fitted to depict information in digital systems, such as computers, as it can simply be portrayed using electrical signals. As a consequence, knowledge of how to convert among the decimal and binary systems is important for computer programmers and for solving mathematical problems including huge numbers.
While the process of converting decimal to binary can be time-consuming and vulnerable to errors when worked on manually, there are tools that can easily change between the two systems.
