The decimal and binary number systems are the world’s most frequently utilized number systems today.
The decimal system, also under the name of the base-10 system, is the system we use in our daily lives. It utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. At the same time, the binary system, also known as the base-2 system, utilizes only two figures (0 and 1) to represent numbers.
Learning how to transform from and to the decimal and binary systems are vital for many reasons. For example, computers utilize the binary system to portray data, so software programmers are supposed to be expert in changing between the two systems.
Furthermore, comprehending how to change between the two systems can helpful to solve mathematical problems including large numbers.
This blog article will cover the formula for converting decimal to binary, provide a conversion chart, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of transforming a decimal number to a binary number is done manually using the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) found in the prior step by 2, and document the quotient and the remainder.
Repeat the prior steps until the quotient is equivalent to 0.
The binary equivalent of the decimal number is achieved by inverting the sequence of the remainders acquired in the prior steps.
This may sound complex, so here is an example to illustrate this method:
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 acquired by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table portraying 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 instances 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 equivalent of 25 is 11001, that is obtained by inverting 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, which is achieved by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined earlier provide a way to manually change decimal to binary, it can be tedious and open to error for big numbers. Luckily, other methods can be used to swiftly and effortlessly change decimals to binary.
For instance, you can utilize the built-in features in a calculator or a spreadsheet program to change decimals to binary. You could additionally use web-based applications for instance binary converters, that allow you to input 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 constraints contrast to the decimal system.
For example, the binary system fails to represent fractions, so it is solely suitable for representing whole numbers.
The binary system also 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, that has six digits. The extended string of 0s and 1s could be inclined to typing errors and reading errors.
Final Thoughts on Decimal to Binary
Despite these limitations, the binary system has a lot of merits over the decimal system. For instance, the binary system is lot easier than the decimal system, as it just uses two digits. This simpleness makes it easier to conduct mathematical operations 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. As a result, understanding how to convert between the decimal and binary systems is essential for computer programmers and for unraveling mathematical problems involving huge numbers.
Even though the process of changing decimal to binary can be tedious and vulnerable to errors when done manually, there are applications which can quickly convert within the two systems.
