The decimal and binary number systems are the world’s most frequently utilized number systems today.
The decimal system, also under the name of the base-10 system, is the system we utilize in our everyday lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. At the same time, the binary system, also called the base-2 system, employees only two figures (0 and 1) to depict numbers.
Comprehending how to convert between the decimal and binary systems are essential for multiple reasons. For example, computers use the binary system to depict data, so software programmers are supposed to be proficient in changing between the two systems.
Furthermore, learning how to change between the two systems can help solve mathematical problems concerning enormous numbers.
This blog article will go through the formula for converting decimal to binary, offer a conversion chart, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The procedure of transforming 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 prior step by 2, and document the quotient and the remainder.
Replicate the prior steps until the quotient is similar to 0.
The binary equivalent of the decimal number is achieved by inverting the sequence of the remainders acquired in the previous steps.
This may sound complicated, so here is an example to illustrate 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 equivalent of 75 is 1001011, which is obtained by inverting 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 some examples of decimal to binary transformation employing 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 inverting 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 acquired by inverting the invert 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 labor-intensive and error-prone for big numbers. Thankfully, other ways can be employed to swiftly and effortlessly change decimals to binary.
For example, you can utilize the incorporated functions in a spreadsheet or a calculator program to convert decimals to binary. You can additionally use web-based applications for instance binary converters, which allow you to enter a decimal number, and the converter will spontaneously produce the equivalent binary number.
It is worth noting 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 fit for representing whole numbers.
The binary system further requires more digits to represent a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, that has six digits. The extended string of 0s and 1s could be prone to typos and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has a lot of 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 easier to conduct mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further fitted to representing information in digital systems, such as computers, as it can easily be depicted utilizing electrical signals. As a result, knowledge of how to transform between the decimal and binary systems is important for computer programmers and for unraveling mathematical problems concerning large numbers.
While the process of converting decimal to binary can be tedious and vulnerable to errors when done manually, there are applications which can rapidly convert among the two systems.
