The decimal and binary number systems are the world’s most frequently used number systems today.
The decimal system, also known as the base-10 system, is the system we utilize in our everyday lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. However, the binary system, also known as the base-2 system, employees only two digits (0 and 1) to depict numbers.
Comprehending how to transform from and to the decimal and binary systems are essential for many reasons. For example, computers use the binary system to depict data, so software programmers must be expert in changing within the two systems.
Additionally, understanding how to convert among the two systems can be beneficial to solve mathematical questions involving large numbers.
This article will go through the formula for converting decimal to binary, give a conversion table, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The method of changing a decimal number to a binary number is performed manually utilizing the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) collect in the last step by 2, and note the quotient and the remainder.
Repeat the previous steps before the quotient is equivalent to 0.
The binary equal of the decimal number is acquired by inverting the series of the remainders received in the prior steps.
This might sound confusing, 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 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 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 steps talked about priorly:
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 gained 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 equivalent of 128 is 10000000, which is obtained by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps defined above provide a way to manually convert decimal to binary, it can be tedious and error-prone for large numbers. Fortunately, other methods can be utilized to swiftly and easily convert decimals to binary.
For instance, you can employ the incorporated functions in a spreadsheet or a calculator application to convert decimals to binary. You can additionally utilize web-based tools similar to binary converters, which allow you to type a decimal number, and the converter will spontaneously generate the respective binary number.
It is worth pointing out that the binary system has handful of limitations compared to the decimal system.
For example, the binary system is unable to represent fractions, so it is only appropriate for representing whole numbers.
The binary system additionally requires 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 long string of 0s and 1s can be prone to typos and reading errors.
Last Thoughts on Decimal to Binary
In spite of these limitations, the binary system has a lot of 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 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 effortlessly be represented utilizing electrical signals. Consequently, understanding how to change among the decimal and binary systems is important for computer programmers and for solving mathematical questions including large numbers.
While the process of converting decimal to binary can be tedious and prone with error when worked on manually, there are applications which can quickly convert between the two systems.
