The decimal and binary number systems are the world’s most commonly used number systems today.
The decimal system, also under the name of the base-10 system, is the system we utilize in our everyday lives. It utilizes ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. On the other hand, the binary system, also known as the base-2 system, employees only two figures (0 and 1) to portray numbers.
Learning how to convert between the decimal and binary systems are important for multiple reasons. For example, computers utilize the binary system to portray data, so software engineers are supposed to be expert in changing between the two systems.
Furthermore, understanding how to convert among the two systems can help solve math problems concerning enormous numbers.
This article will go through the formula for changing decimal to binary, give a conversion table, and give instances of decimal to binary conversion.
Formula for Changing 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) obtained in the previous step by 2, and note the quotient and the remainder.
Reiterate the prior steps until the quotient is similar to 0.
The binary equal of the decimal number is obtained by inverting the sequence of the remainders received in the previous steps.
This may sound complex, so here is an example to illustrate 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 reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table 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 examples of decimal to binary transformation 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 gained by inverting the series 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 equal of 128 is 10000000, that is acquired by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined above offers a method to manually convert decimal to binary, it can be time-consuming and error-prone for large numbers. Fortunately, other methods can be employed to rapidly and simply change decimals to binary.
For instance, you can use the built-in features in a spreadsheet or a calculator application to convert decimals to binary. You can additionally use web tools for instance binary converters, that enables you to input a decimal number, and the converter will automatically generate the corresponding binary number.
It is worth noting that the binary system has few limitations compared to the decimal system.
For example, the binary system cannot represent fractions, so it is only fit for dealing with whole numbers.
The binary system further requires more digits to represent a number than the decimal system. For instance, the decimal number 100 can be represented by the binary number 1100100, which has six digits. The length string of 0s and 1s can be liable to typos and reading errors.
Final Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has several advantages with the decimal system. For example, the binary system is much simpler than the decimal system, as it just utilizes two digits. This simplicity makes it easier to conduct mathematical functions 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 simply be portrayed using electrical signals. As a result, knowledge of how to change between the decimal and binary systems is important for computer programmers and for solving mathematical problems including large numbers.
Even though the process of converting decimal to binary can be labor-intensive and error-prone when worked on manually, there are applications which can rapidly change among the two systems.
