The decimal and binary number systems are the world’s most frequently used number systems presently.
The decimal system, also known as 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 portray numbers. On the other hand, the binary system, also called the base-2 system, utilizes only two digits (0 and 1) to represent numbers.
Comprehending how to transform from and to the decimal and binary systems are vital for many reasons. For example, computers use the binary system to portray data, so software programmers should be expert in converting within the two systems.
Additionally, comprehending how to convert between the two systems can be beneficial to solve mathematical questions concerning enormous numbers.
This blog will cover the formula for transforming decimal to binary, offer a conversion chart, and give instances 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 utilizing the following steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) obtained in the last step by 2, and record the quotient and the remainder.
Reiterate the prior steps before the quotient is equal to 0.
The binary equivalent of the decimal number is obtained by reversing the order of the remainders acquired in the prior steps.
This may sound complicated, so here is an example to portray 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 obtained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table depicting 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 some examples of decimal to binary transformation utilizing the steps discussed earlier:
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, that 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 equal of 128 is 10000000, that is achieved by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps outlined prior provide a method to manually change decimal to binary, it can be time-consuming and prone to error for big numbers. Luckily, other systems can be employed to rapidly and easily change decimals to binary.
For example, you can utilize the built-in functions in a calculator or a spreadsheet program to convert decimals to binary. You could also use web-based applications for instance binary converters, that allow you to type a decimal number, and the converter will automatically produce the equivalent binary number.
It is worth pointing out that the binary system has handful of limitations compared to the decimal system.
For instance, the binary system cannot portray fractions, so it is solely fit for representing whole numbers.
The binary system additionally requires more digits to represent a number than the decimal system. For instance, the decimal number 100 can be portrayed by the binary number 1100100, which has six digits. The long string of 0s and 1s can be inclined to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Despite these restrictions, the binary system has a lot of advantages over the decimal system. For instance, the binary system is far simpler than the decimal system, as it just utilizes 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 more suited to depict information in digital systems, such as computers, as it can easily be represented utilizing electrical signals. Consequently, knowledge of how to change between the decimal and binary systems is essential for computer programmers and for unraveling mathematical questions including large numbers.
Even though the process of converting decimal to binary can be tedious and prone with error when worked on manually, there are tools which can quickly change within the two systems.
