The decimal and binary number systems are the world’s most commonly used number systems today.
The decimal system, also under the name of the base-10 system, is the system we use in our everyday lives. It uses ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. On the other hand, the binary system, also called the base-2 system, utilizes only two figures (0 and 1) to depict numbers.
Understanding how to transform from and to the decimal and binary systems are important for many reasons. For instance, computers use the binary system to depict data, so computer engineers must be proficient in converting within the two systems.
Furthermore, learning how to change between the two systems can be beneficial to solve math problems concerning large numbers.
This blog will cover the formula for transforming decimal to binary, provide a conversion table, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The procedure of changing a decimal number to a binary number is done manually utilizing the ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) collect in the previous step by 2, and document the quotient and the remainder.
Replicate the prior steps before the quotient is similar to 0.
The binary equal of the decimal number is obtained by reversing the order of the remainders obtained in the previous steps.
This might 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 inverting 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 few examples of decimal to binary conversion using the method talked about 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, which is gained by reversing 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 equal of 128 is 10000000, which is acquired by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps defined above offers a method to manually convert decimal to binary, it can be tedious and prone to error for big numbers. Luckily, other systems can be used to quickly and simply convert decimals to binary.
For instance, you could employ the built-in features in a calculator or a spreadsheet application to convert decimals to binary. You can also utilize web applications similar to binary converters, which enables you to type a decimal number, and the converter will automatically produce the corresponding binary number.
It is important to note that the binary system has few limitations contrast to the decimal system.
For instance, the binary system is unable to portray fractions, so it is only suitable for dealing with whole numbers.
The binary system further 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, that has six digits. The extended string of 0s and 1s could be inclined to typos and reading errors.
Final Thoughts on Decimal to Binary
Despite these limitations, the binary system has several advantages over the decimal system. For example, the binary system is lot easier than the decimal system, as it only utilizes two digits. This simpleness makes it easier to carry out mathematical operations in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is more suited to representing information in digital systems, such as computers, as it can effortlessly be depicted utilizing electrical signals. Consequently, knowledge of how to change among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems including large numbers.
While the method of converting decimal to binary can be tedious and error-prone when worked on manually, there are applications that can quickly convert between the two systems.
