The decimal and binary number systems are the world’s most commonly used number systems right now.
The decimal system, also known as the base-10 system, is the system we utilize in our everyday lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. At the same time, the binary system, also called the base-2 system, uses only two digits (0 and 1) to represent numbers.
Comprehending how to transform from and to the decimal and binary systems are essential for many reasons. For example, computers utilize the binary system to portray data, so computer engineers should be competent in converting among the two systems.
In addition, comprehending how to change within the two systems can help solve math questions including large numbers.
This article will cover the formula for transforming decimal to binary, offer a conversion table, and give instances 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 record the quotient and the remainder.
Divide the quotient (only) obtained in the previous step by 2, and document the quotient and the remainder.
Repeat the last steps before the quotient is equal to 0.
The binary equal of the decimal number is achieved by inverting the order of the remainders acquired in the prior steps.
This may sound confusing, so here is an example to show you 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 gained 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 examples of decimal to binary transformation utilizing the method discussed 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 acquired by reversing 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 achieved by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described above provide a way to manually change decimal to binary, it can be tedious and open to error for big numbers. Thankfully, other systems can be used to swiftly and simply change decimals to binary.
For example, you can utilize the incorporated features in a spreadsheet or a calculator application to change decimals to binary. You could further use web-based applications for instance binary converters, which allow you to enter a decimal number, and the converter will automatically generate the equivalent binary number.
It is worth pointing out that the binary system has some constraints compared to the decimal system.
For example, the binary system is unable to illustrate fractions, so it is solely appropriate for representing whole numbers.
The binary system additionally requires more digits to portray a number than the decimal system. For example, the decimal number 100 can be represented by the binary number 1100100, that has six digits. The extended string of 0s and 1s could be inclined to typos and reading errors.
Final Thoughts on Decimal to Binary
Regardless these limits, the binary system has several merits over the decimal system. For example, the binary system is much simpler than the decimal system, as it just uses two digits. This simplicity makes it easier to perform mathematical operations 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 depicted using electrical signals. Consequently, knowledge of how to convert among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical questions concerning large numbers.
While the method of changing decimal to binary can be labor-intensive and vulnerable to errors when worked on manually, there are tools that can easily change among the two systems.
