The decimal and binary number systems are the world’s most frequently 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 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 depict numbers.
Learning how to transform from and to the decimal and binary systems are vital for many reasons. For instance, computers utilize the binary system to represent data, so software engineers should be expert in changing within the two systems.
Furthermore, learning how to change within the two systems can be beneficial to solve mathematical questions involving large numbers.
This blog will go through the formula for changing decimal to binary, provide a conversion chart, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The method of changing a decimal number to a binary number is done manually utilizing the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) collect in the last step by 2, and note the quotient and the remainder.
Repeat the prior steps unless the quotient is equivalent to 0.
The binary corresponding of the decimal number is obtained by inverting the series of the remainders obtained in the last steps.
This may sound complicated, 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 acquired by inverting 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 few examples of decimal to binary conversion using the steps talked about 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, 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 equal of 128 is 10000000, that is obtained by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described prior offers a way to manually change decimal to binary, it can be time-consuming and prone to error for big numbers. Thankfully, other systems can be employed to quickly and easily convert decimals to binary.
For instance, you can utilize the built-in functions in a calculator or a spreadsheet application to convert decimals to binary. You can additionally use online tools similar to binary converters, that enables you to input a decimal number, and the converter will automatically produce the equivalent binary number.
It is worth pointing out that the binary system has few limitations compared to the decimal system.
For example, the binary system is unable to represent fractions, so it is solely fit for representing whole numbers.
The binary system further needs more digits to portray a number than the decimal system. For example, the decimal number 100 can be portrayed by the binary number 1100100, which has six digits. The extended string of 0s and 1s could be inclined to typing errors and reading errors.
Final Thoughts on Decimal to Binary
In spite of these limits, the binary system has several advantages over the decimal system. For example, the binary system is much simpler than the decimal system, as it only utilizes two digits. This simplicity makes it simpler to perform mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further fitted to representing information in digital systems, such as computers, as it can simply be depicted using electrical signals. As a consequence, understanding how to transform between the decimal and binary systems is crucial for computer programmers and for solving mathematical problems including huge numbers.
While the method of converting decimal to binary can be tedious and vulnerable to errors when done manually, there are applications that can easily change within the two systems.
