The decimal and binary number systems are the world’s most frequently utilized number systems today.
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 illustrate numbers. At the same time, the binary system, also called the base-2 system, utilizes only two figures (0 and 1) to represent 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 computer engineers are supposed to be proficient in changing within the two systems.
Additionally, understanding how to change between the two systems can be beneficial to solve mathematical problems involving enormous numbers.
This blog will go through 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 process of changing a decimal number to a binary number is done manually utilizing the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) obtained in the prior step by 2, and document the quotient and the remainder.
Reiterate the previous steps unless the quotient is similar to 0.
The binary equivalent of the decimal number is obtained by inverting the sequence of the remainders acquired in the prior steps.
This might sound complex, so here is an example to show you this method:
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 gained by inverting the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table portraying 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 examples of decimal to binary transformation using the steps talked about 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 equivalent of 25 is 11001, which 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 equivalent of 128 is 10000000, that is obtained by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps outlined above provide a way to manually convert decimal to binary, it can be labor-intensive and error-prone for big numbers. Fortunately, other methods can be employed to rapidly and effortlessly convert decimals to binary.
For instance, you can employ the built-in features in a calculator or a spreadsheet application to convert decimals to binary. You could additionally use web applications such as binary converters, which enables you to enter a decimal number, and the converter will automatically generate the respective binary number.
It is important to note that the binary system has few constraints compared to the decimal system.
For instance, the binary system fails to represent fractions, so it is solely suitable for representing whole numbers.
The binary system additionally 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, which has six digits. The length string of 0s and 1s could be liable to typing errors and reading errors.
Last Thoughts on Decimal to Binary
Regardless these limitations, the binary system has several advantages with the decimal system. For example, the binary system is lot easier than the decimal system, as it only utilizes two digits. This simpleness makes it simpler to carry out 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 simply be represented utilizing electrical signals. As a consequence, knowledge of how to convert between the decimal and binary systems is important for computer programmers and for solving mathematical problems concerning large numbers.
Even though the process of converting decimal to binary can be labor-intensive and error-prone when done manually, there are applications that can easily change among the two systems.
