The decimal and binary number systems are the world’s most frequently used number systems right now.
The decimal system, also called the base-10 system, is the system we use in our everyday lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. However, the binary system, also known as the base-2 system, utilizes only two figures (0 and 1) to represent numbers.
Comprehending how to transform from and to the decimal and binary systems are vital for various reasons. For instance, computers use the binary system to depict data, so software programmers must be proficient in changing among the two systems.
Furthermore, understanding how to change among the two systems can helpful to solve mathematical questions concerning enormous numbers.
This blog article will cover the formula for changing decimal to binary, offer a conversion table, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The method of transforming a decimal number to a binary number is done manually utilizing the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) obtained in the last step by 2, and record the quotient and the remainder.
Repeat the last steps unless the quotient is similar to 0.
The binary corresponding of the decimal number is acquired by inverting the order of the remainders acquired in the previous steps.
This may sound complicated, so here is an example to illustrate this method:
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 obtained by reversing 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 few examples of decimal to binary transformation employing the method discussed earlier:
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 acquired by inverting 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 equal of 128 is 10000000, which is achieved by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps outlined above offers a way to manually convert decimal to binary, it can be time-consuming and error-prone for big numbers. Thankfully, other methods can be utilized to swiftly and easily change decimals to binary.
For example, you could use the built-in functions in a calculator or a spreadsheet application to convert decimals to binary. You can also utilize online tools similar to binary converters, which allow you to type a decimal number, and the converter will automatically produce the corresponding binary number.
It is worth noting that the binary system has some 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 also needs more digits to portray a number than the decimal system. For instance, the decimal number 100 can be represented by the binary number 1100100, which has six digits. The extended string of 0s and 1s can be prone to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Despite these restrictions, the binary system has several merits over the decimal system. For instance, the binary system is far simpler than the decimal system, as it only uses two digits. This simplicity makes it easier to conduct mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is further fitted to depict information in digital systems, such as computers, as it can effortlessly be depicted utilizing electrical signals. As a consequence, knowledge of how to change among the decimal and binary systems is important for computer programmers and for unraveling mathematical problems involving large numbers.
Even though the process of converting decimal to binary can be tedious and error-prone when done manually, there are tools that can easily change among the two systems.
