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 utilize in our everyday lives. It employees 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, uses only two digits (0 and 1) to represent numbers.
Comprehending how to transform from and to the decimal and binary systems are important for many reasons. For instance, computers use the binary system to depict data, so software programmers should be proficient in changing within the two systems.
Additionally, learning how to convert among the two systems can help solve math problems concerning enormous numbers.
This blog will go through the formula for converting decimal to binary, offer a conversion table, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The method of changing a decimal number to a binary number is performed manually utilizing 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 record the quotient and the remainder.
Reiterate the prior steps unless the quotient is similar to 0.
The binary corresponding of the decimal number is achieved by reversing the series of the remainders obtained 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 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 table showing 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 using the method 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, which 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 equal of 128 is 10000000, which is acquired by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined earlier provide a way to manually convert decimal to binary, it can be time-consuming and prone to error for big numbers. Luckily, other methods can be utilized to rapidly and effortlessly change decimals to binary.
For example, you could use the incorporated functions in a calculator or a spreadsheet program to change decimals to binary. You could further utilize online applications similar to binary converters, which enables you to enter a decimal number, and the converter will spontaneously generate the corresponding binary number.
It is important to note that the binary system has some constraints contrast to the decimal system.
For instance, the binary system is unable to represent fractions, so it is only appropriate for dealing with whole numbers.
The binary system further needs more digits to illustrate 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 prone to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Regardless these limitations, the binary system has a lot of advantages over the decimal system. For example, the binary system is lot easier than the decimal system, as it just 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 portrayed utilizing electrical signals. As a result, understanding how to convert between the decimal and binary systems is important for computer programmers and for solving mathematical questions concerning huge numbers.
Although the process of converting decimal to binary can be labor-intensive and error-prone when worked on manually, there are tools which can rapidly change among the two systems.
