The decimal and binary number systems are the world’s most frequently used 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 represent numbers. However, 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 important for multiple reasons. For instance, computers use the binary system to portray data, so software programmers must be proficient in changing between the two systems.
In addition, learning how to convert among the two systems can help solve math questions including large numbers.
This blog article will go through the formula for changing decimal to binary, give a conversion table, 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 utilizing the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) collect 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 equivalent of the decimal number is obtained by reversing the order of the remainders acquired 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 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 examples of decimal to binary transformation employing the method discussed earlier:
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 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 equivalent of 128 is 10000000, which is obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps defined earlier offers a way to manually change decimal to binary, it can be tedious and open to error for big numbers. Fortunately, other methods can be employed to swiftly and easily convert decimals to binary.
For example, you can utilize the incorporated features in a spreadsheet or a calculator program to change decimals to binary. You could also utilize web-based tools such as binary converters, which allow you to enter a decimal number, and the converter will automatically generate the respective binary number.
It is important to note that the binary system has some limitations compared to the decimal system.
For instance, the binary system cannot illustrate fractions, so it is solely fit for representing 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 portrayed by the binary number 1100100, which has six digits. The extended string of 0s and 1s could be inclined to typing errors and reading errors.
Final Thoughts on Decimal to Binary
Despite these limitations, the binary system has a lot of advantages with the decimal system. For instance, the binary system is much simpler than the decimal system, as it just utilizes two digits. This simpleness makes it easier to conduct mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is more suited to representing information in digital systems, such as computers, as it can simply be depicted utilizing electrical signals. As a result, understanding how to convert 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 labor-intensive and prone with error when worked on manually, there are applications that can quickly convert among the two systems.
