The decimal and binary number systems are the world’s most frequently utilized number systems today.
The decimal system, also known as the base-10 system, is the system we use in our daily lives. It utilizes ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. On the other hand, the binary system, also called the base-2 system, utilizes only two figures (0 and 1) to depict numbers.
Learning how to transform from and to the decimal and binary systems are vital for many reasons. For instance, computers utilize the binary system to represent data, so computer engineers are supposed to be competent in changing within the two systems.
Furthermore, comprehending how to convert between the two systems can helpful to solve math problems concerning large numbers.
This blog will go through the formula for transforming decimal to binary, provide a conversion table, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The process of changing a decimal number to a binary number is performed manually utilizing the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) collect in the previous step by 2, and note the quotient and the remainder.
Repeat the last steps until the quotient is equivalent to 0.
The binary equal of the decimal number is obtained by inverting the series of the remainders received in the last steps.
This may sound complex, so here is an example to illustrate this process:
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 equivalent 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 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 conversion utilizing the steps 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 equal of 25 is 11001, which is gained by reversing 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 equivalent of 128 is 10000000, which is achieved by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps described above offers a way to manually change decimal to binary, it can be tedious and error-prone for large numbers. Thankfully, other ways can be used to rapidly and easily convert decimals to binary.
For example, you could use the built-in features in a spreadsheet or a calculator application to convert decimals to binary. You can also utilize web-based tools such as binary converters, which allow you to type a decimal number, and the converter will spontaneously generate the corresponding binary number.
It is worth noting that the binary system has handful of limitations contrast to the decimal system.
For example, the binary system fails to represent 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 instance, the decimal number 100 can be represented by the binary number 1100100, that has six digits. The length string of 0s and 1s can be liable to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these limits, the binary system has several advantages with the decimal system. For example, the binary system is far simpler than the decimal system, as it just uses two digits. This simplicity makes it simpler to perform mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is further fitted to depict information in digital systems, such as computers, as it can simply be represented using electrical signals. As a result, knowledge of how to convert among the decimal and binary systems is essential for computer programmers and for solving mathematical problems including large numbers.
Although the method of converting decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are tools which can easily convert within the two systems.
