The decimal and binary number systems are the world’s most frequently utilized number systems right now.
The decimal system, also under the name of 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 portray numbers. However, the binary system, also called the base-2 system, uses only two figures (0 and 1) to portray numbers.
Learning how to transform from and to the decimal and binary systems are essential for various reasons. For example, computers use the binary system to represent data, so software programmers should be expert in changing between the two systems.
Additionally, learning how to change within the two systems can be beneficial to solve math problems concerning enormous numbers.
This article will cover the formula for converting 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 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.
Replicate the previous steps before the quotient is similar to 0.
The binary corresponding of the decimal number is obtained by inverting the sequence of the remainders acquired 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 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 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 some 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 equal of 25 is 11001, which is obtained 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 inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described above provide a method to manually change decimal to binary, it can be time-consuming and open to error for large numbers. Thankfully, other ways can be used to swiftly and effortlessly convert decimals to binary.
For example, you can utilize the built-in features in a spreadsheet or a calculator program to convert decimals to binary. You can also utilize web applications such as binary converters, which allow you to input a decimal number, and the converter will spontaneously generate the respective binary number.
It is important to note that the binary system has some constraints in comparison to the decimal system.
For example, the binary system fails to illustrate fractions, so it is solely suitable for representing 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 represented by the binary number 1100100, that has six digits. The long string of 0s and 1s could be liable to typing errors and reading errors.
Final Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has a lot of merits over the decimal system. For instance, the binary system is lot easier than the decimal system, as it just uses two digits. This simplicity makes it simpler to perform mathematical operations in the binary system, for example 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 utilizing electrical signals. Consequently, knowledge of how to convert among the decimal and binary systems is crucial for computer programmers and for solving mathematical questions concerning large numbers.
While the method of converting decimal to binary can be time-consuming and vulnerable to errors when worked on manually, there are applications that can quickly convert within the two systems.
