The decimal and binary number systems are the world’s most commonly utilized number systems right now.
The decimal system, also called the base-10 system, is the system we use in our daily lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. However, the binary system, also called the base-2 system, uses only two figures (0 and 1) to depict numbers.
Understanding how to convert between the decimal and binary systems are vital for many reasons. For example, computers utilize the binary system to represent data, so computer engineers are supposed to be proficient in converting between the two systems.
Additionally, comprehending how to change within the two systems can help solve math questions concerning enormous numbers.
This article will go through the formula for transforming decimal to binary, provide a conversion chart, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of transforming a decimal number to a binary number is done manually utilizing the following steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) found in the last step by 2, and record the quotient and the remainder.
Replicate the previous steps until the quotient is similar to 0.
The binary equivalent of the decimal number is obtained by inverting the series of the remainders obtained in the last steps.
This might sound confusing, so here is an example to show you 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 obtained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart 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 some examples of decimal to binary conversion using the steps discussed earlier:
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 equal of 25 is 11001, which is gained 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 acquired by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described prior offers a method to manually convert decimal to binary, it can be time-consuming and open to error for large numbers. Thankfully, other ways can be utilized to quickly and effortlessly convert decimals to binary.
For instance, you could employ the incorporated features in a calculator or a spreadsheet application to change decimals to binary. You could also utilize web applications for instance binary converters, which enables you to input a decimal number, and the converter will spontaneously generate the corresponding binary number.
It is worth noting that the binary system has few limitations compared to the decimal system.
For instance, the binary system is unable to illustrate fractions, so it is only fit for dealing with whole numbers.
The binary system additionally needs more digits to illustrate a number than the decimal system. For example, 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 inclined to typos and reading errors.
Final Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has a lot of merits over the decimal system. For example, the binary system is far simpler than the decimal system, as it only utilizes two digits. This simplicity makes it easier to conduct mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more fitted to representing information in digital systems, such as computers, as it can simply be depicted utilizing electrical signals. As a consequence, understanding how to transform between the decimal and binary systems is essential for computer programmers and for solving mathematical problems including huge numbers.
Even though the process of changing decimal to binary can be time-consuming and error-prone when worked on manually, there are tools which can easily change between the two systems.
