The decimal and binary number systems are the world’s most frequently utilized number systems today.
The decimal system, also known as the base-10 system, is the system we utilize in our everyday lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate 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.
Learning how to transform from and to the decimal and binary systems are vital for various reasons. For example, computers use the binary system to portray data, so computer programmers are supposed to be expert in changing within the two systems.
Furthermore, comprehending how to convert among the two systems can be beneficial to solve mathematical questions concerning large numbers.
This blog article will go through the formula for converting decimal to binary, offer a conversion chart, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of converting a decimal number to a binary number is performed manually using the following 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 document the quotient and the remainder.
Reiterate the previous steps until the quotient is equivalent to 0.
The binary corresponding of the decimal number is obtained by inverting the order of the remainders acquired in the last steps.
This may sound confusing, so here is an example to show you this process:
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 inverting 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 some instances of decimal to binary conversion employing the steps discussed 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, that is acquired 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 equal of 128 is 10000000, which is acquired by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps defined prior provide a method to manually convert decimal to binary, it can be tedious and prone to error for big numbers. Fortunately, other methods can be used to swiftly and simply convert decimals to binary.
For instance, you can use the built-in features in a calculator or a spreadsheet program to change decimals to binary. You can additionally use web-based applications such as binary converters, that allow you to input a decimal number, and the converter will automatically generate the corresponding binary number.
It is worth pointing out that the binary system has few limitations in comparison to the decimal system.
For example, the binary system fails to represent fractions, so it is solely fit for dealing with whole numbers.
The binary system also requires more digits to illustrate 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 could be inclined to typing errors and reading errors.
Final Thoughts on Decimal to Binary
In spite of these limits, the binary system has several advantages with the decimal system. For example, the binary system is much simpler than the decimal system, as it just uses two digits. This simpleness makes it easier to conduct mathematical operations in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further suited to depict information in digital systems, such as computers, as it can effortlessly be portrayed utilizing electrical signals. Consequently, knowledge of how to change among the decimal and binary systems is important for computer programmers and for solving mathematical problems including huge numbers.
Although the method of changing decimal to binary can be tedious and error-prone when done manually, there are tools that can easily change within the two systems.
