The decimal and binary number systems are the world’s most commonly utilized number systems right now.
The decimal system, also under the name of the base-10 system, is the system we use in our daily lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. At the same time, the binary system, also called the base-2 system, utilizes only two figures (0 and 1) to portray numbers.
Learning how to transform from and to the decimal and binary systems are essential for many reasons. For example, computers use the binary system to depict data, so software programmers should be proficient in converting within the two systems.
Additionally, learning how to change within the two systems can be beneficial to solve math problems including enormous numbers.
This blog will cover the formula for converting decimal to binary, offer a conversion table, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The method of converting a decimal number to a binary number is done manually using the ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) found in the last step by 2, and document the quotient and the remainder.
Reiterate the last steps before the quotient is similar to 0.
The binary equivalent of the decimal number is acquired by inverting the series of the remainders received in the prior steps.
This may sound confusing, so here is an example to illustrate 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 equivalent of 75 is 1001011, which is acquired by reversing 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 instances of decimal to binary transformation utilizing the steps talked about priorly:
Example 1: Change 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 equal of 128 is 10000000, which is obtained by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps described earlier offers a way to manually change decimal to binary, it can be labor-intensive and prone to error for large numbers. Fortunately, other ways can be utilized to rapidly and easily change decimals to binary.
For instance, you could utilize the built-in functions in a spreadsheet or a calculator application to change decimals to binary. You could additionally utilize web tools such as binary converters, which enables you to enter a decimal number, and the converter will automatically produce the respective binary number.
It is important to note that the binary system has handful of limitations compared to the decimal system.
For instance, the binary system is unable to illustrate fractions, so it is only fit for dealing with whole numbers.
The binary system additionally requires more digits to represent a number than the decimal system. For example, the decimal number 100 can be represented by the binary number 1100100, that has six digits. The extended string of 0s and 1s could be liable to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Despite these limits, the binary system has several merits with the decimal system. For instance, the binary system is much simpler than the decimal system, as it just utilizes two digits. This simpleness makes it simpler to carry out mathematical operations 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 easily be portrayed utilizing electrical signals. Consequently, knowledge of how to transform between the decimal and binary systems is essential for computer programmers and for solving mathematical problems including large numbers.
Even though the process of converting decimal to binary can be time-consuming and vulnerable to errors when done manually, there are tools that can quickly change within the two systems.
