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 utilize in our daily lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. At the same time, the binary system, also called the base-2 system, employees only two digits (0 and 1) to portray numbers.
Understanding how to transform from and to the decimal and binary systems are essential for various reasons. For example, computers use the binary system to portray data, so software engineers are supposed to be expert in changing between the two systems.
Furthermore, comprehending how to convert between the two systems can helpful to solve math problems including large numbers.
This blog will go through the formula for transforming decimal to binary, provide a conversion table, and give examples 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 account the quotient and the remainder.
Divide the quotient (only) collect in the prior step by 2, and record the quotient and the remainder.
Repeat the last steps before the quotient is similar to 0.
The binary corresponding of the decimal number is obtained by reversing the sequence of the remainders acquired in the previous steps.
This may sound confusing, so here is an example to portray 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 equivalent of 75 is 1001011, which is acquired 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 examples of decimal to binary conversion using the steps talked about 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 obtained 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 reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined earlier provide a method to manually convert decimal to binary, it can be time-consuming and open to error for large numbers. Fortunately, other systems can be employed to swiftly and easily change decimals to binary.
For example, you could employ the incorporated features in a calculator or a spreadsheet application to convert decimals to binary. You can also utilize web applications such as binary converters, which enables you to input a decimal number, and the converter will automatically generate the respective binary number.
It is worth pointing out that the binary system has some constraints compared to the decimal system.
For instance, the binary system is unable to represent fractions, so it is solely appropriate for dealing with whole numbers.
The binary system additionally needs more digits to portray a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The length string of 0s and 1s can be prone to typos and reading errors.
Concluding Thoughts on Decimal to Binary
Despite these limitations, the binary system has some merits with the decimal system. For instance, the binary system is much simpler than the decimal system, as it just uses two digits. This simpleness makes it easier to carry out mathematical functions in the binary system, such as 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 represented utilizing electrical signals. As a result, knowledge of how to convert among the decimal and binary systems is essential for computer programmers and for unraveling mathematical problems concerning huge numbers.
Although the method of changing decimal to binary can be labor-intensive and vulnerable to errors when worked on manually, there are applications which can quickly change among the two systems.
