The decimal and binary number systems are the world’s most frequently utilized number systems today.
The decimal system, also called the base-10 system, is the system we use in our everyday lives. It employees ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. On the other hand, the binary system, also known as the base-2 system, uses only two figures (0 and 1) to depict numbers.
Understanding how to convert between the decimal and binary systems are essential for multiple reasons. For example, computers use the binary system to represent data, so software programmers should be proficient in converting between the two systems.
Furthermore, comprehending how to convert between the two systems can be beneficial to solve math questions involving enormous numbers.
This blog article will cover the formula for transforming decimal to binary, offer a conversion chart, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The method of transforming a decimal number to a binary number is performed manually using 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 note the quotient and the remainder.
Replicate the previous steps until the quotient is similar to 0.
The binary equivalent of the decimal number is achieved by reversing the sequence of the remainders received in the last steps.
This might sound complex, 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 gained 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 few examples of decimal to binary transformation utilizing the steps talked about priorly:
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, that is gained 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 reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps outlined earlier offers a way to manually convert decimal to binary, it can be time-consuming and error-prone for large numbers. Luckily, other methods can be utilized to swiftly and effortlessly change decimals to binary.
For instance, you can utilize the built-in functions in a spreadsheet or a calculator application to convert decimals to binary. You could further use online applications similar to binary converters, that enables you to type a decimal number, and the converter will spontaneously produce the equivalent binary number.
It is worth pointing out that the binary system has handful of limitations compared to the decimal system.
For instance, the binary system cannot portray fractions, so it is only appropriate for dealing with whole numbers.
The binary system additionally needs more digits to illustrate 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 length string of 0s and 1s could be prone to typing errors and reading errors.
Final Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has some merits over the decimal system. For instance, the binary system is far simpler than the decimal system, as it just utilizes two digits. This simpleness makes it simpler to perform mathematical operations 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 portrayed using electrical signals. As a consequence, knowledge of how to transform among the decimal and binary systems is essential for computer programmers and for unraveling mathematical problems including huge numbers.
Although the method of changing decimal to binary can be time-consuming and vulnerable to errors when worked on manually, there are tools that can quickly change among the two systems.
