The decimal and binary number systems are the world’s most frequently utilized number systems presently.
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 illustrate numbers. At the same time, the binary system, also known as the base-2 system, utilizes only two digits (0 and 1) to represent numbers.
Understanding how to convert between the decimal and binary systems are important for many reasons. For instance, computers use the binary system to depict data, so software engineers must be expert in changing between the two systems.
Additionally, comprehending how to change among the two systems can helpful to solve math problems including large numbers.
This blog will cover the formula for transforming decimal to binary, offer a conversion chart, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of transforming a decimal number to a binary number is done 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 document the quotient and the remainder.
Reiterate the prior steps unless the quotient is equal to 0.
The binary equal of the decimal number is achieved by inverting the order of the remainders received in the last steps.
This may sound confusing, so here is an example to show you 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 chart portraying 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 transformation employing the steps discussed priorly:
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 gained by inverting the sequence 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 achieved by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps defined above offers a method to manually convert decimal to binary, it can be time-consuming and prone to error for large numbers. Fortunately, other ways can be employed to rapidly and easily convert decimals to binary.
For instance, you could utilize the built-in features in a calculator or a spreadsheet program to convert decimals to binary. You can additionally use web applications such as binary converters, that allow you to enter a decimal number, and the converter will spontaneously generate the equivalent binary number.
It is worth pointing out that the binary system has few limitations compared to the decimal system.
For instance, the binary system is unable to portray fractions, so it is only appropriate for dealing with whole numbers.
The binary system also needs more digits to represent a number than the decimal system. For example, the decimal number 100 can be portrayed by the binary number 1100100, which has six digits. The length string of 0s and 1s can be liable to typos and reading errors.
Final Thoughts on Decimal to Binary
In spite of these limitations, the binary system has some advantages over the decimal system. For example, the binary system is far simpler than the decimal system, as it just utilizes two digits. This simplicity makes it simpler to perform mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further suited to representing information in digital systems, such as computers, as it can simply be portrayed utilizing electrical signals. As a result, knowledge of how to change between the decimal and binary systems is important for computer programmers and for unraveling mathematical questions concerning large numbers.
Even though the method of changing decimal to binary can be labor-intensive and prone with error when worked on manually, there are tools that can quickly convert between the two systems.
