The decimal and binary number systems are the world’s most commonly utilized number systems presently.
The decimal system, also called 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, uses only two digits (0 and 1) to portray numbers.
Learning how to transform from and to the decimal and binary systems are important for many reasons. For example, computers use the binary system to depict data, so computer programmers are supposed to be expert in converting within the two systems.
In addition, understanding how to convert among the two systems can helpful to solve math problems including large numbers.
This article will cover the formula for converting decimal to binary, offer a conversion chart, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The procedure of changing a decimal number to a binary number is done 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.
Replicate the last steps until the quotient is similar to 0.
The binary equal of the decimal number is obtained by reversing the series of the remainders obtained in the prior steps.
This might sound complicated, so here is an example to illustrate 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 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 few instances of decimal to binary transformation employing the steps 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, which is acquired by inverting 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 achieved by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described prior provide a way to manually change decimal to binary, it can be labor-intensive and open to error for large numbers. Fortunately, other methods can be employed to quickly and simply change decimals to binary.
For example, you can use the built-in functions in a calculator or a spreadsheet application to convert decimals to binary. You could further utilize web-based tools for instance binary converters, that allow you to type a decimal number, and the converter will spontaneously generate the equivalent binary number.
It is important to note that the binary system has some limitations contrast to the decimal system.
For example, the binary system fails to represent fractions, so it is solely fit for representing whole numbers.
The binary system further requires more digits to portray a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, that has six digits. The extended string of 0s and 1s can be prone to typos and reading errors.
Last Thoughts on Decimal to Binary
Despite these limitations, the binary system has some merits over the decimal system. For example, the binary system is much simpler than the decimal system, as it just uses two digits. This simpleness makes it easier to perform mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is more fitted to depict information in digital systems, such as computers, as it can easily be depicted using electrical signals. As a result, knowledge of how to change between the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems involving huge numbers.
Even though the method of changing decimal to binary can be tedious and error-prone when worked on manually, there are applications which can quickly convert within the two systems.
