The decimal and binary number systems are the world’s most commonly utilized number systems today.
The decimal system, also known as the base-10 system, is the system we utilize in our daily lives. It utilizes ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. At the same time, the binary system, also called the base-2 system, utilizes only two digits (0 and 1) to represent numbers.
Learning how to transform from and to the decimal and binary systems are vital for various reasons. For example, computers use the binary system to depict data, so computer engineers should be expert in converting between the two systems.
Additionally, learning how to convert within the two systems can help solve math questions concerning large 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 Converting Decimal to Binary
The method of converting a decimal number to a binary number is done manually utilizing the ensuing steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) found in the previous step by 2, and document the quotient and the remainder.
Repeat the last steps until the quotient is equal to 0.
The binary corresponding of the decimal number is acquired by reversing the sequence of the remainders acquired in the prior steps.
This might sound complicated, so here is an example to show you this method:
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 portraying 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 conversion utilizing the steps talked about earlier:
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 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 prior offers a way to manually convert decimal to binary, it can be time-consuming and prone to error for large numbers. Thankfully, other methods can be employed to swiftly and effortlessly convert decimals to binary.
For example, you could employ the built-in features in a calculator or a spreadsheet application to change decimals to binary. You could further utilize web-based applications similar to binary converters, which enables you to type a decimal number, and the converter will spontaneously produce the respective binary number.
It is important to note that the binary system has some constraints in comparison to the decimal system.
For instance, the binary system cannot represent fractions, so it is only fit for dealing with 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 could be prone to typing errors and reading errors.
Final Thoughts on Decimal to Binary
In spite of these limits, the binary system has some merits with the decimal system. For example, the binary system is far simpler than the decimal system, as it only utilizes two digits. This simpleness makes it simpler to conduct mathematical operations in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is further fitted to representing information in digital systems, such as computers, as it can effortlessly be depicted utilizing electrical signals. As a result, understanding how to change among the decimal and binary systems is crucial for computer programmers and for solving mathematical questions including large numbers.
Although the method of converting decimal to binary can be tedious and error-prone when done manually, there are tools which can quickly convert within the two systems.
