The decimal and binary number systems are the world’s most commonly utilized number systems right now.
The decimal system, also called 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. At the same time, the binary system, also known as the base-2 system, uses only two digits (0 and 1) to represent numbers.
Comprehending how to convert between the decimal and binary systems are important for various reasons. For instance, computers use the binary system to depict data, so computer engineers must be expert in converting within the two systems.
Additionally, understanding how to convert among the two systems can helpful to solve mathematical problems involving enormous numbers.
This blog article will cover the formula for changing decimal to binary, provide a conversion table, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The procedure of changing a decimal number to a binary number is performed manually utilizing the following steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) obtained in the prior step by 2, and document the quotient and the remainder.
Replicate the previous steps unless the quotient is similar to 0.
The binary corresponding of the decimal number is acquired by reversing the order of the remainders obtained in the prior steps.
This may sound complicated, 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 inverting the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table 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 using 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 equivalent of 25 is 11001, that is obtained 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 achieved by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps defined earlier provide a method to manually convert decimal to binary, it can be tedious and open to error for big numbers. Thankfully, other ways can be used to quickly and effortlessly convert decimals to binary.
For instance, you can utilize the built-in features in a spreadsheet or a calculator program to change decimals to binary. You could also use online applications similar to binary converters, that allow you to enter a decimal number, and the converter will automatically generate the corresponding binary number.
It is worth noting that the binary system has some limitations contrast to the decimal system.
For example, the binary system cannot portray fractions, so it is solely appropriate for representing whole numbers.
The binary system additionally needs more digits to portray a number than the decimal system. For example, the decimal number 100 can be portrayed by the binary number 1100100, which has six digits. The long string of 0s and 1s can be prone to typos 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 uses two digits. This simplicity makes it simpler to conduct 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 effortlessly be depicted using electrical signals. As a consequence, understanding how to convert between the decimal and binary systems is essential for computer programmers and for unraveling mathematical questions involving large numbers.
While the method of converting decimal to binary can be time-consuming and error-prone when done manually, there are applications that can rapidly convert among the two systems.
