The decimal and binary number systems are the world’s most frequently used number systems today.
The decimal system, also under the name of 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. However, the binary system, also known as the base-2 system, uses only two figures (0 and 1) to represent numbers.
Learning how to transform from and to the decimal and binary systems are essential for many reasons. For example, computers use the binary system to represent data, so software engineers are supposed to be competent in converting between the two systems.
Additionally, understanding how to convert among the two systems can help solve math problems concerning enormous numbers.
This article will go through the formula for changing decimal to binary, offer a conversion chart, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The method of converting a decimal number to a binary number is performed manually utilizing the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) obtained in the previous step by 2, and document the quotient and the remainder.
Replicate the prior steps unless the quotient is equivalent to 0.
The binary corresponding of the decimal number is obtained by inverting the series of the remainders obtained in the prior steps.
This might sound confusing, so here is an example to illustrate 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 equal 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 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 few examples of decimal to binary conversion using 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, 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 equivalent of 128 is 10000000, which is obtained by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined prior provide a way to manually change decimal to binary, it can be time-consuming and error-prone for large numbers. Luckily, other ways can be utilized to quickly and easily convert decimals to binary.
For example, you could utilize the built-in functions in a spreadsheet or a calculator application to convert decimals to binary. You could also utilize online tools for instance binary converters, that enables you to enter a decimal number, and the converter will automatically generate the respective binary number.
It is important to note that the binary system has few limitations contrast to the decimal system.
For example, the binary system fails to represent fractions, so it is only appropriate for dealing with whole numbers.
The binary system further needs more digits to represent a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, that has six digits. The length string of 0s and 1s could be liable to typing errors and reading errors.
Last Thoughts on Decimal to Binary
Regardless these limits, the binary system has several advantages with the decimal system. For instance, the binary system is far simpler than the decimal system, as it just utilizes two digits. This simpleness makes it easier to conduct mathematical functions in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is further suited to depict information in digital systems, such as computers, as it can easily be represented using electrical signals. Consequently, understanding how to transform among the decimal and binary systems is essential for computer programmers and for solving mathematical problems concerning large numbers.
Even though the method of changing decimal to binary can be tedious and vulnerable to errors when done manually, there are tools which can easily change within the two systems.
