The decimal and binary number systems are the world’s most frequently used number systems today.
The decimal system, also called the base-10 system, is the system we use in our daily lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. However, 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 instance, computers use the binary system to depict data, so computer programmers must be expert in converting between the two systems.
Additionally, learning how to change between the two systems can be beneficial to solve math questions involving enormous numbers.
This blog article will cover the formula for transforming decimal to binary, provide a conversion table, 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 using the following steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) found in the last step by 2, and note the quotient and the remainder.
Repeat the previous steps unless the quotient is similar to 0.
The binary equivalent of the decimal number is obtained by reversing the sequence of the remainders acquired in the last steps.
This might sound confusing, 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 equal of 75 is 1001011, which is acquired by inverting the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart 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 some instances of decimal to binary conversion utilizing 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, that is achieved by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined prior provide a way to manually convert decimal to binary, it can be labor-intensive and error-prone for big numbers. Thankfully, other methods can be used to rapidly and easily convert decimals to binary.
For instance, you could employ the incorporated features in a spreadsheet or a calculator application to change decimals to binary. You can further use web tools similar to binary converters, which enables you to input a decimal number, and the converter will spontaneously produce the corresponding binary number.
It is worth pointing out that the binary system has handful of constraints in comparison to the decimal system.
For example, the binary system is unable to portray 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 example, the decimal number 100 can be portrayed by the binary number 1100100, which has six digits. The length string of 0s and 1s can be inclined to typos and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these restrictions, 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 simpleness makes it simpler to perform mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is more fitted to representing information in digital systems, such as computers, as it can easily be depicted using electrical signals. As a result, understanding how to transform between the decimal and binary systems is important for computer programmers and for unraveling mathematical problems including huge numbers.
While the process of converting decimal to binary can be labor-intensive and vulnerable to errors when worked on manually, there are tools which can rapidly change among the two systems.
