The decimal and binary number systems are the world’s most commonly used number systems presently.
The decimal system, also called the base-10 system, is the system we utilize in our daily lives. It utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. At the same time, the binary system, also known as the base-2 system, uses only two digits (0 and 1) to represent numbers.
Understanding how to transform from and to the decimal and binary systems are essential for many reasons. For example, computers utilize the binary system to represent data, so computer programmers are supposed to be proficient in changing within the two systems.
Furthermore, learning how to change between the two systems can helpful to solve mathematical questions including large numbers.
This blog article will cover the formula for converting decimal to binary, provide a conversion chart, 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 done manually using the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) found in the prior step by 2, and note the quotient and the remainder.
Reiterate the last steps before the quotient is equivalent to 0.
The binary equivalent of the decimal number is achieved by inverting the order of the remainders obtained in the last steps.
This may sound complicated, so here is an example to illustrate 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 reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table 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 few examples of decimal to binary transformation utilizing the steps 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 gained by reversing the series of remainders (1, 1, 0, 0, 1).
Example 2: Change 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, that is acquired by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps defined earlier provide a method to manually change decimal to binary, it can be labor-intensive and prone to error for big numbers. Luckily, other ways can be used to quickly and effortlessly convert decimals to binary.
For example, you could use the incorporated features in a calculator or a spreadsheet application to convert decimals to binary. You can additionally use web applications such as binary converters, that enables you to input a decimal number, and the converter will spontaneously produce the corresponding binary number.
It is important to note that the binary system has some limitations in comparison to the decimal system.
For example, the binary system is unable to portray fractions, so it is solely fit for dealing with whole numbers.
The binary system further requires more digits to illustrate 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 extended string of 0s and 1s can be prone to typos and reading errors.
Final Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has several merits with the decimal system. For example, the binary system is much simpler than the decimal system, as it only utilizes two digits. This simplicity makes it simpler to perform mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further fitted to depict information in digital systems, such as computers, as it can effortlessly be represented using electrical signals. As a consequence, understanding how to convert between the decimal and binary systems is important for computer programmers and for solving mathematical problems involving huge numbers.
While the process of changing decimal to binary can be labor-intensive and error-prone when worked on manually, there are tools that can rapidly change among the two systems.
