The decimal and binary number systems are the world’s most frequently used number systems presently.
The decimal system, also under the name of the base-10 system, is the system we utilize in our everyday lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. However, the binary system, also known as the base-2 system, utilizes only two figures (0 and 1) to depict numbers.
Learning how to transform from and to the decimal and binary systems are essential for many reasons. For instance, computers utilize the binary system to represent data, so software engineers are supposed to be expert in changing between the two systems.
Furthermore, understanding how to change within the two systems can help solve mathematical problems including large numbers.
This article will cover the formula for converting 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 performed manually utilizing the following 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.
Repeat the prior steps unless the quotient is similar to 0.
The binary equal of the decimal number is acquired by inverting the sequence of the remainders acquired in the last steps.
This might sound confusing, so here is an example to portray 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 equivalent of 75 is 1001011, which is acquired by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table depicting 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 transformation utilizing the method 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, which is obtained by inverting 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 equivalent of 128 is 10000000, which is achieved by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps defined prior offers a way to manually change decimal to binary, it can be labor-intensive and open to error for big numbers. Luckily, other systems can be utilized to quickly and easily change decimals to binary.
For example, you could use the incorporated functions in a calculator or a spreadsheet application to convert decimals to binary. You could additionally use web tools such as binary converters, which allow you to enter a decimal number, and the converter will automatically generate the corresponding binary number.
It is worth pointing out that the binary system has few constraints in comparison to the decimal system.
For instance, the binary system is unable to represent fractions, so it is only fit for dealing with whole numbers.
The binary system also requires more digits to portray 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 could be prone to typing errors and reading errors.
Last Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has a lot of advantages with the decimal system. For example, the binary system is much simpler than the decimal system, as it only utilizes two digits. This simpleness makes it simpler to carry out mathematical operations in the binary system, for instance 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 portrayed utilizing electrical signals. As a consequence, knowledge of how to change among the decimal and binary systems is crucial for computer programmers and for solving mathematical problems involving huge numbers.
While the method of converting decimal to binary can be time-consuming and error-prone when done manually, there are tools that can quickly change among the two systems.
