The decimal and binary number systems are the world’s most commonly used number systems presently.
The decimal system, also under the name of the base-10 system, is the system we use in our daily lives. It employees ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. However, the binary system, also known as the base-2 system, uses only two digits (0 and 1) to depict numbers.
Learning how to transform from and to the decimal and binary systems are vital for multiple reasons. For example, computers utilize the binary system to represent data, so computer engineers must be expert in converting among the two systems.
Furthermore, learning how to convert between the two systems can helpful to solve mathematical problems concerning enormous numbers.
This blog article will go through the formula for converting decimal to binary, give a conversion table, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The method 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 prior step by 2, and note the quotient and the remainder.
Repeat the previous steps before the quotient is equivalent to 0.
The binary equal of the decimal number is achieved by reversing the order of the remainders obtained in the prior steps.
This may sound complicated, so here is an example to portray 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 equal of 75 is 1001011, which is gained by inverting the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart portraying 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 instances of decimal to binary conversion utilizing 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 equal of 25 is 11001, that is acquired by inverting the sequence 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 reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps defined above provide a way to manually convert decimal to binary, it can be tedious and error-prone for big numbers. Luckily, other systems can be utilized to quickly and easily change decimals to binary.
For instance, you could use the built-in features in a calculator or a spreadsheet application to convert decimals to binary. You can also utilize web-based applications such as binary converters, that allow you to input a decimal number, and the converter will automatically produce the corresponding binary number.
It is worth noting that the binary system has handful of constraints compared to the decimal system.
For example, the binary system fails to illustrate fractions, so it is only fit for dealing with 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 represented by the binary number 1100100, which has six digits. The length string of 0s and 1s could be inclined to typing errors and reading errors.
Last Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has some merits with the decimal system. For instance, the binary system is lot easier than the decimal system, as it only uses two digits. This simpleness makes it simpler to carry out mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more fitted to representing information in digital systems, such as computers, as it can simply be depicted using electrical signals. Consequently, understanding how to convert among the decimal and binary systems is essential for computer programmers and for unraveling mathematical problems including huge numbers.
Even though the process of converting decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are applications that can quickly change between the two systems.
