The decimal and binary number systems are the world’s most commonly used number systems right now.
The decimal system, also under the name of 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. On the other hand, the binary system, also known as the base-2 system, utilizes only two digits (0 and 1) to portray numbers.
Comprehending how to convert between the decimal and binary systems are vital for multiple reasons. For instance, computers use the binary system to represent data, so software programmers should be expert in changing among the two systems.
Furthermore, comprehending how to convert between the two systems can help solve mathematical questions concerning large numbers.
This article will cover the formula for changing decimal to binary, offer a conversion chart, and give instances 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 using the ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) obtained in the previous step by 2, and record the quotient and the remainder.
Reiterate the last steps until the quotient is equal to 0.
The binary equivalent of the decimal number is acquired by reversing the sequence of the remainders received in the last steps.
This might sound complicated, so here is an example to illustrate 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 obtained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table depicting 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 transformation employing the steps discussed priorly:
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 gained 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, that is obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps described above provide a way to manually change decimal to binary, it can be time-consuming and open to error for big numbers. Fortunately, other ways can be employed to rapidly and easily convert decimals to binary.
For example, you could use the built-in features in a spreadsheet or a calculator application to change decimals to binary. You can additionally use online applications for instance binary converters, which enables you to type a decimal number, and the converter will automatically produce the respective binary number.
It is worth noting that the binary system has few limitations in comparison to the decimal system.
For instance, the binary system is unable to represent fractions, so it is only suitable for representing whole numbers.
The binary system further requires more digits to portray a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, that has six digits. The long string of 0s and 1s could be prone to typing errors and reading errors.
Final Thoughts on Decimal to Binary
In spite of these limitations, the binary system has a lot of advantages with the decimal system. For instance, the binary system is lot easier than the decimal system, as it only uses two digits. This simplicity 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 effortlessly be represented using electrical signals. Consequently, knowledge of how to convert among the decimal and binary systems is essential for computer programmers and for solving mathematical questions including huge numbers.
Although the method of converting decimal to binary can be tedious and vulnerable to errors when done manually, there are applications that can rapidly convert within the two systems.
