The decimal and binary number systems are the world’s most commonly used number systems presently.
The decimal system, also called the base-10 system, is the system we utilize in our daily lives. It uses ten figures (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 figures (0 and 1) to depict numbers.
Understanding how to transform from and to the decimal and binary systems are important for multiple reasons. For example, computers utilize the binary system to depict data, so software programmers are supposed to be competent in converting within the two systems.
Furthermore, understanding how to convert within the two systems can be beneficial to solve math questions concerning enormous numbers.
This blog will cover the formula for converting decimal to binary, offer a conversion table, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The process of changing a decimal number to a binary number is done manually using the ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) found in the previous step by 2, and note the quotient and the remainder.
Repeat the last steps until the quotient is similar to 0.
The binary equivalent of the decimal number is acquired by inverting the series of the remainders received in the prior steps.
This might sound complicated, 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 equivalent 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 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 some instances of decimal to binary transformation utilizing 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 equal of 25 is 11001, that is gained by reversing the sequence 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 equal of 128 is 10000000, which is acquired by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps defined above offers a way to manually change decimal to binary, it can be labor-intensive and prone to error for big numbers. Luckily, other ways can be employed to rapidly and simply change decimals to binary.
For instance, you could utilize the built-in features in a spreadsheet or a calculator application to convert decimals to binary. You can further utilize web-based tools similar to binary converters, that allow you to enter a decimal number, and the converter will automatically generate the equivalent binary number.
It is worth noting that the binary system has some limitations in comparison to the decimal system.
For instance, the binary system fails to portray fractions, so it is solely suitable for representing whole numbers.
The binary system further needs more digits to illustrate a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The length string of 0s and 1s can be liable to typos and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has some advantages over the decimal system. For instance, the binary system is lot easier than the decimal system, as it only uses two digits. This simpleness makes it simpler to perform 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. As a result, knowledge of how to change among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical questions including large numbers.
Although the process of converting decimal to binary can be labor-intensive and vulnerable to errors when worked on manually, there are applications that can rapidly change within the two systems.
