The decimal and binary number systems are the world’s most commonly utilized number systems today.
The decimal system, also called the base-10 system, is the system we use in our daily lives. It utilizes 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, utilizes only two digits (0 and 1) to portray numbers.
Understanding how to convert between the decimal and binary systems are vital for many reasons. For instance, computers use the binary system to portray data, so software engineers should be competent in changing within the two systems.
In addition, understanding how to convert among the two systems can help solve math problems including enormous numbers.
This blog will go through the formula for converting decimal to binary, provide a conversion table, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The process of transforming a decimal number to a binary number is performed manually utilizing the ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) obtained in the last step by 2, and document the quotient and the remainder.
Replicate the last steps until the quotient is equal to 0.
The binary equal of the decimal number is achieved by reversing the series of the remainders acquired in the previous steps.
This may sound confusing, so here is an example to portray 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 acquired by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table showing 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 conversion utilizing the method discussed priorly:
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 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, which is achieved by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described prior provide a way to manually change decimal to binary, it can be labor-intensive and prone to error for big numbers. Thankfully, other methods can be employed to rapidly and easily convert decimals to binary.
For example, you can utilize the incorporated features in a spreadsheet or a calculator program to convert decimals to binary. You can further utilize web applications similar to binary converters, which allow you to enter a decimal number, and the converter will spontaneously generate the equivalent binary number.
It is worth noting that the binary system has some limitations compared to the decimal system.
For example, the binary system cannot portray fractions, so it is only appropriate for dealing with whole numbers.
The binary system also needs more digits to portray 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 length string of 0s and 1s could be liable to typos and reading errors.
Concluding Thoughts on Decimal to Binary
Despite these limitations, the binary system has a lot of merits 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, such as addition, subtraction, multiplication, and division.
The binary system is more fitted to depict information in digital systems, such as computers, as it can simply be represented using electrical signals. Consequently, knowledge of how to transform among the decimal and binary systems is essential for computer programmers and for unraveling mathematical questions involving large numbers.
Although the process of changing decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are applications which can easily change within the two systems.
