The decimal and binary number systems are the world’s most commonly used number systems presently.
The decimal system, also under the name of 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 represent numbers. At the same time, the binary system, also known as the base-2 system, employees only two digits (0 and 1) to depict numbers.
Comprehending how to convert between the decimal and binary systems are vital for many reasons. For instance, computers utilize the binary system to depict data, so software engineers are supposed to be proficient in converting between the two systems.
In addition, comprehending how to change within the two systems can help solve math problems involving enormous numbers.
This 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 procedure of converting a decimal number to a binary number is performed manually utilizing the following steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) obtained in the previous step by 2, and note the quotient and the remainder.
Repeat the previous steps until the quotient is equal to 0.
The binary equal of the decimal number is obtained by inverting the sequence of the remainders received in the prior steps.
This may sound complicated, so here is an example to show you this method:
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 inverting 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 instances of decimal to binary conversion employing the steps talked about priorly:
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, which is acquired by reversing the series 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 equivalent of 128 is 10000000, which is achieved by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined above provide a method to manually change decimal to binary, it can be time-consuming and open to error for large numbers. Fortunately, other methods can be used to swiftly and simply convert decimals to binary.
For example, you could employ the built-in features in a calculator or a spreadsheet application to convert decimals to binary. You can additionally utilize web tools for instance binary converters, that allow you to input a decimal number, and the converter will automatically generate the equivalent binary number.
It is important to note that the binary system has handful of constraints compared to the decimal system.
For example, the binary system fails to represent fractions, so it is solely suitable for dealing with whole numbers.
The binary system further needs more digits to represent a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The length string of 0s and 1s could be liable to typos and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these limitations, 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 simplicity makes it simpler to carry out mathematical operations 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 depicted utilizing electrical signals. As a consequence, understanding how to transform among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems including large numbers.
Although the method of changing decimal to binary can be tedious and prone with error when done manually, there are applications which can quickly change within the two systems.
