The decimal and binary number systems are the world’s most frequently used number systems today.
The decimal system, also called the base-10 system, is the system we use in our everyday lives. It employees ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. However, the binary system, also called the base-2 system, employees only two figures (0 and 1) to represent numbers.
Learning how to convert between the decimal and binary systems are vital for multiple reasons. For example, computers use the binary system to depict data, so software engineers should be expert in changing between the two systems.
Additionally, learning how to convert among the two systems can helpful to solve math questions including enormous numbers.
This article will go through the formula for changing decimal to binary, give a conversion table, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of changing a decimal number to a binary number is performed manually using the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) found in the previous step by 2, and note the quotient and the remainder.
Replicate the last steps before the quotient is similar to 0.
The binary equivalent of the decimal number is acquired by inverting the sequence of the remainders obtained in the last steps.
This might sound confusing, so here is an example to portray this process:
Let’s change 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 chart depicting 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 some examples of decimal to binary transformation utilizing the steps 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 equal of 25 is 11001, which is gained by reversing 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 equal of 128 is 10000000, which is achieved by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined earlier offers a way to manually change decimal to binary, it can be time-consuming and prone to error for large numbers. Fortunately, other ways can be used to rapidly and easily convert decimals to binary.
For example, you could employ the built-in features in a calculator or a spreadsheet program to convert decimals to binary. You could additionally utilize web-based applications for instance binary converters, that enables you to input a decimal number, and the converter will spontaneously generate the respective binary number.
It is worth noting that the binary system has few constraints compared to the decimal system.
For instance, the binary system is unable to illustrate fractions, so it is only appropriate for representing whole numbers.
The binary system further needs more digits to illustrate a number than the decimal system. For example, the decimal number 100 can be represented by the binary number 1100100, which has six digits. The extended string of 0s and 1s can be inclined to typos and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these limitations, the binary system has some merits over the decimal system. For instance, the binary system is much simpler than the decimal system, as it just uses two digits. This simplicity makes it simpler to conduct mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is further fitted to depict information in digital systems, such as computers, as it can simply be depicted using electrical signals. As a consequence, knowledge of how to convert among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems involving huge numbers.
Although the process of converting decimal to binary can be labor-intensive and error-prone when worked on manually, there are tools that can rapidly convert between the two systems.
