The decimal and binary number systems are the world’s most frequently utilized number systems right now.
The decimal system, also called the base-10 system, is the system we utilize in our daily lives. It employees ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. On the other hand, the binary system, also known as the base-2 system, utilizes only two figures (0 and 1) to portray numbers.
Comprehending how to convert between the decimal and binary systems are essential for various reasons. For example, computers utilize the binary system to portray data, so software programmers must be expert in changing between the two systems.
In addition, comprehending how to change within the two systems can helpful to solve mathematical problems involving enormous numbers.
This article will go through the formula for transforming decimal to binary, provide a conversion chart, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of changing a decimal number to a binary number is done manually utilizing the following steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) collect in the last step by 2, and record the quotient and the remainder.
Replicate the previous steps unless the quotient is similar to 0.
The binary equivalent of the decimal number is obtained by reversing the sequence of the remainders obtained in the prior steps.
This may sound complicated, 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 equal of 75 is 1001011, which is gained by inverting the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart showing 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 transformation using the method discussed earlier:
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, that is gained by reversing the sequence 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 achieved by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps defined earlier offers a way to manually convert decimal to binary, it can be time-consuming and prone to error for large numbers. Fortunately, other ways can be used to rapidly and easily convert decimals to binary.
For example, you can employ the incorporated features in a spreadsheet or a calculator application to change decimals to binary. You can further utilize web applications similar to binary converters, which allow you to enter a decimal number, and the converter will automatically produce the respective binary number.
It is worth pointing out that the binary system has some constraints contrast to the decimal system.
For instance, the binary system fails to illustrate fractions, so it is solely appropriate for representing whole numbers.
The binary system also requires more digits to illustrate 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 prone to typos and reading errors.
Final Thoughts on Decimal to Binary
Regardless these limitations, the binary system has several advantages with the decimal system. For instance, the binary system is much simpler than the decimal system, as it only utilizes two digits. This simplicity makes it simpler to perform mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further fitted to depict information in digital systems, such as computers, as it can easily be portrayed using electrical signals. Consequently, knowledge of how to transform among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical questions involving large numbers.
Although the method of changing decimal to binary can be labor-intensive and error-prone when worked on manually, there are applications that can rapidly change within the two systems.
