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 use in our everyday 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, employees only two digits (0 and 1) to portray numbers.
Understanding how to convert between the decimal and binary systems are vital for many reasons. For instance, computers use the binary system to represent data, so computer programmers must be competent in converting within the two systems.
Furthermore, learning how to convert between the two systems can be beneficial to solve mathematical problems including enormous numbers.
This article will cover the formula for converting decimal to binary, give a conversion table, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The method of converting a decimal number to a binary number is done manually using the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) found in the prior step by 2, and document the quotient and the remainder.
Reiterate the prior steps before the quotient is similar to 0.
The binary equivalent of the decimal number is achieved by reversing the sequence of the remainders received in the prior steps.
This might sound complicated, so here is an example to portray 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 acquired by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart 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 few examples of decimal to binary conversion utilizing the steps talked about 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, which is obtained by reversing the series 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).
Although the steps outlined earlier provide a method to manually change decimal to binary, it can be time-consuming and prone to error for large numbers. Thankfully, other methods can be used to swiftly and simply convert decimals to binary.
For instance, you can employ the built-in features in a spreadsheet or a calculator application to change decimals to binary. You could additionally utilize online applications such as binary converters, which allow you to type a decimal number, and the converter will automatically generate the respective binary number.
It is worth pointing out that the binary system has few constraints compared to the decimal system.
For instance, the binary system cannot represent fractions, so it is solely suitable for representing whole numbers.
The binary system further needs more digits to represent 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 long string of 0s and 1s could be liable to typos and reading errors.
Concluding Thoughts on Decimal to Binary
Despite these limits, the binary system has a lot of advantages over the decimal system. For example, the binary system is far simpler than the decimal system, as it only uses two digits. This simpleness makes it easier to conduct mathematical operations in the binary system, such as 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 represented using electrical signals. As a result, knowledge of how to transform between the decimal and binary systems is essential for computer programmers and for solving mathematical questions involving large numbers.
While the method of converting decimal to binary can be tedious and prone with error when worked on manually, there are tools that can rapidly change among the two systems.
