The decimal and binary number systems are the world’s most frequently utilized number systems presently.
The decimal system, also known as the base-10 system, is the system we utilize in our daily lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. On the other hand, the binary system, also known as the base-2 system, utilizes only two figures (0 and 1) to represent numbers.
Comprehending how to transform from and to the decimal and binary systems are essential for many reasons. For instance, computers utilize the binary system to represent data, so software engineers must be expert in changing within the two systems.
In addition, understanding how to change within the two systems can help solve mathematical problems including enormous numbers.
This blog article will go through 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 utilizing the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) collect in the previous step by 2, and record the quotient and the remainder.
Replicate the last steps unless the quotient is similar to 0.
The binary equivalent of the decimal number is achieved by inverting the series of the remainders received in the prior steps.
This might sound complex, 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 chart 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 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 equivalent of 25 is 11001, that is acquired 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 obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps described earlier provide a method to manually convert decimal to binary, it can be tedious and error-prone for big numbers. Thankfully, other ways can be employed to rapidly and effortlessly change decimals to binary.
For instance, you can use the built-in features in a calculator or a spreadsheet application to change decimals to binary. You could also use web-based applications similar to binary converters, which enables you to type a decimal number, and the converter will automatically generate the corresponding binary number.
It is important to note that the binary system has handful of limitations in comparison to the decimal system.
For example, the binary system is unable to illustrate fractions, so it is only appropriate for dealing with 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 represented by the binary number 1100100, that has six digits. The extended string of 0s and 1s can be prone to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Despite these limits, the binary system has several advantages with the decimal system. For instance, 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, 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 effortlessly be represented utilizing electrical signals. As a consequence, understanding how to transform between the decimal and binary systems is essential for computer programmers and for unraveling mathematical questions involving huge numbers.
Even though the method of converting decimal to binary can be tedious and prone with error when worked on manually, there are tools that can easily change between the two systems.
