The decimal and binary number systems are the world’s most frequently used 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. However, the binary system, also called the base-2 system, uses only two figures (0 and 1) to portray numbers.
Understanding how to convert between the decimal and binary systems are essential for many reasons. For example, computers use the binary system to depict data, so software programmers are supposed to be proficient in changing within the two systems.
Furthermore, comprehending how to change within the two systems can be beneficial to solve math questions involving enormous numbers.
This blog will cover the formula for changing decimal to binary, offer a conversion chart, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The process of transforming 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) found in the last step by 2, and document the quotient and the remainder.
Reiterate the previous steps before the quotient is equivalent to 0.
The binary equivalent of the decimal number is acquired by reversing the order of the remainders acquired in the prior steps.
This might sound complicated, so here is an example to show you 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 equivalent 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 table showing 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 priorly:
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 obtained by reversing the sequence 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 equivalent of 128 is 10000000, that is acquired by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps defined earlier provide a way to manually change decimal to binary, it can be time-consuming and error-prone for large numbers. Luckily, other methods can be employed to quickly and easily convert decimals to binary.
For instance, you can employ the incorporated functions in a spreadsheet or a calculator program to convert decimals to binary. You can further utilize online applications for instance binary converters, that enables you to enter a decimal number, and the converter will spontaneously generate the equivalent binary number.
It is important to note that the binary system has some constraints compared to the decimal system.
For instance, the binary system fails to represent fractions, so it is solely suitable for representing whole numbers.
The binary system also needs more digits to represent a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, that has six digits. The long string of 0s and 1s could be inclined to typing errors and reading errors.
Last Thoughts on Decimal to Binary
In spite of these limitations, the binary system has some advantages with the decimal system. For instance, the binary system is much simpler than the decimal system, as it just utilizes two digits. This simplicity makes it simpler to conduct mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further suited to representing information in digital systems, such as computers, as it can effortlessly be represented utilizing electrical signals. Consequently, knowledge of how to change between the decimal and binary systems is crucial for computer programmers and for solving mathematical problems including huge numbers.
Although the process of changing decimal to binary can be time-consuming and vulnerable to errors when done manually, there are tools that can quickly convert between the two systems.
