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 uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. However, the binary system, also called the base-2 system, utilizes only two figures (0 and 1) to portray numbers.
Learning how to convert between the decimal and binary systems are important for many reasons. For example, computers utilize the binary system to depict data, so software programmers should be expert in changing within the two systems.
In addition, learning how to convert within the two systems can help solve mathematical questions involving enormous numbers.
This blog will go through the formula for converting decimal to binary, give a conversion table, and give instances 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 using the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) found in the last step by 2, and document the quotient and the remainder.
Reiterate the last steps until the quotient is equivalent to 0.
The binary equal of the decimal number is achieved by inverting the order of the remainders received in the last steps.
This may sound complicated, 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 equal of 75 is 1001011, which is gained 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 few instances of decimal to binary conversion employing the method talked about priorly:
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 equal of 25 is 11001, which is gained by reversing 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, that is achieved by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps outlined above provide a method to manually change decimal to binary, it can be labor-intensive and prone to error for large numbers. Luckily, other ways can be utilized to quickly and effortlessly convert decimals to binary.
For example, you can use the incorporated features in a calculator or a spreadsheet application to change decimals to binary. You can also utilize web applications for instance binary converters, that allow you to type a decimal number, and the converter will automatically generate the corresponding binary number.
It is worth pointing out that the binary system has some limitations compared to the decimal system.
For example, the binary system cannot represent fractions, so it is solely fit for representing whole numbers.
The binary system also 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 can be liable to typos and reading errors.
Last Thoughts on Decimal to Binary
Regardless these limitations, the binary system has some merits over the decimal system. For instance, the binary system is much 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 further fitted to representing information in digital systems, such as computers, as it can effortlessly be depicted using electrical signals. As a consequence, understanding how to transform between the decimal and binary systems is essential for computer programmers and for unraveling mathematical problems including huge numbers.
While the method of converting decimal to binary can be labor-intensive and error-prone when worked on manually, there are applications which can rapidly convert among the two systems.
