The decimal and binary number systems are the world’s most commonly utilized number systems presently.
The decimal system, also known as the base-10 system, is the system we use in our everyday lives. It utilizes ten figures (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, utilizes only two figures (0 and 1) to depict numbers.
Learning how to convert between the decimal and binary systems are vital for various reasons. For instance, computers use the binary system to depict data, so computer engineers must be expert in changing within the two systems.
In addition, comprehending how to change among the two systems can helpful to solve mathematical questions involving 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 method of transforming a decimal number to a binary number is done manually using the ensuing steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) found in the last step by 2, and document the quotient and the remainder.
Replicate the previous steps until the quotient is equal to 0.
The binary equivalent of the decimal number is obtained by reversing the order of the remainders obtained in the previous steps.
This may sound confusing, so here is an example to portray 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 acquired by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table portraying 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 instances 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 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 equivalent of 128 is 10000000, that is achieved by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps outlined above offers a method to manually convert decimal to binary, it can be tedious and error-prone for big numbers. Luckily, other methods can be utilized to quickly and simply change decimals to binary.
For example, you could employ the incorporated features in a spreadsheet or a calculator application to change decimals to binary. You could additionally use online applications similar to binary converters, which allow you to input a decimal number, and the converter will automatically generate the respective binary number.
It is important to note that the binary system has some constraints compared to the decimal system.
For example, the binary system fails to illustrate fractions, so it is solely appropriate for dealing with whole numbers.
The binary system also requires 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 extended string of 0s and 1s can be inclined to typos and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these limits, the binary system has some advantages with the decimal system. For instance, the binary system is far simpler than the decimal system, as it only uses two digits. This simplicity makes it easier to perform mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more suited to depict information in digital systems, such as computers, as it can simply be depicted utilizing electrical signals. As a consequence, knowledge of how to change among the decimal and binary systems is crucial for computer programmers and for solving mathematical questions involving huge numbers.
While the process of changing decimal to binary can be labor-intensive and prone with error when done manually, there are tools that can easily change between the two systems.
