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 use in our daily lives. It uses ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. On the other hand, the binary system, also known as the base-2 system, employees only two digits (0 and 1) to represent numbers.
Learning how to transform from and to the decimal and binary systems are vital for various reasons. For example, computers use the binary system to depict data, so computer engineers are supposed to be competent in changing within the two systems.
In addition, understanding how to change within the two systems can helpful to solve math problems concerning large numbers.
This blog article will cover the formula for transforming decimal to binary, give 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 following steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) collect in the prior step by 2, and document the quotient and the remainder.
Reiterate the prior steps before the quotient is equivalent to 0.
The binary equal of the decimal number is obtained by reversing the series of the remainders received in the last steps.
This may sound complicated, so here is an example to show you 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 reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart depicting 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 employing the method talked about 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 acquired 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, which is acquired by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined prior provide a method to manually change decimal to binary, it can be tedious and open to error for big numbers. Thankfully, other ways can be used to rapidly and simply convert decimals to binary.
For instance, you could use the built-in functions in a calculator or a spreadsheet application to change decimals to binary. You could additionally utilize web applications such as binary converters, that allow you to type a decimal number, and the converter will spontaneously generate the respective binary number.
It is important to note that the binary system has handful of limitations contrast to the decimal system.
For example, the binary system cannot portray fractions, so it is only appropriate for representing whole numbers.
The binary system further requires more digits to represent a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The length string of 0s and 1s could be liable to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these limitations, the binary system has a lot of merits over the decimal system. For instance, the binary system is much simpler than the decimal system, as it only uses two digits. This simplicity makes it easier to perform mathematical functions in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more suited to depict information in digital systems, such as computers, as it can simply be depicted using electrical signals. As a result, understanding how to change between the decimal and binary systems is important for computer programmers and for unraveling mathematical problems involving large numbers.
Even though the process of converting decimal to binary can be time-consuming and error-prone when worked on manually, there are applications which can quickly convert within the two systems.
