The decimal and binary number systems are the world’s most commonly utilized 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 uses 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, uses only two digits (0 and 1) to represent numbers.
Understanding how to transform from and to the decimal and binary systems are important for many reasons. For instance, computers utilize the binary system to depict data, so software programmers must be expert in changing within the two systems.
In addition, learning how to change between the two systems can helpful to solve mathematical problems concerning enormous numbers.
This blog article will cover the formula for transforming 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 using the ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) found in the prior step by 2, and record the quotient and the remainder.
Replicate the previous steps before the quotient is similar to 0.
The binary equal of the decimal number is obtained by reversing the series of the remainders received in the last steps.
This might sound complex, so here is an example to show you 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 gained 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 utilizing the method 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 equivalent of 25 is 11001, that is acquired by reversing 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 equivalent of 128 is 10000000, which is obtained by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined above offers a method to manually convert decimal to binary, it can be time-consuming and open to error for large numbers. Fortunately, other systems can be utilized to quickly and simply convert decimals to binary.
For instance, you can employ the incorporated features in a spreadsheet or a calculator program to change decimals to binary. You could further utilize online 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 worth pointing out that the binary system has few limitations compared to the decimal system.
For instance, the binary system fails to portray fractions, so it is only suitable for dealing with whole numbers.
The binary system also needs more digits to illustrate a number than the decimal system. For example, the decimal number 100 can be represented by the binary number 1100100, that has six digits. The extended string of 0s and 1s could be inclined to typing errors and reading errors.
Last Thoughts on Decimal to Binary
In spite of these limitations, the binary system has some merits over the decimal system. For instance, the binary system is much simpler than the decimal system, as it just utilizes two digits. This simplicity makes it easier to carry out mathematical functions in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more fitted to representing information in digital systems, such as computers, as it can effortlessly be represented utilizing electrical signals. As a consequence, understanding how to transform between the decimal and binary systems is essential for computer programmers and for unraveling mathematical questions including large numbers.
While the process of changing decimal to binary can be labor-intensive and prone with error when done manually, there are applications which can quickly change between the two systems.
