The decimal and binary number systems are the world’s most commonly used number systems today.
The decimal system, also called 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 called the base-2 system, employees only two digits (0 and 1) to depict numbers.
Comprehending how to transform from and to the decimal and binary systems are important for multiple reasons. For instance, computers utilize the binary system to represent data, so computer engineers are supposed to be expert in changing between the two systems.
Furthermore, understanding how to change among the two systems can helpful to solve mathematical questions involving large numbers.
This blog will go through the formula for converting decimal to binary, provide a conversion chart, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The procedure of converting a decimal number to a binary number is done 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 last step by 2, and record the quotient and the remainder.
Repeat the last steps unless the quotient is similar to 0.
The binary equal of the decimal number is obtained by inverting the order of the remainders acquired in the prior steps.
This might sound confusing, so here is an example to illustrate this process:
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 gained by inverting the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table showing 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 few examples of decimal to binary transformation employing the method discussed 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, which is acquired 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, which is obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps defined earlier offers a method to manually change decimal to binary, it can be time-consuming and prone to error for big numbers. Luckily, other systems can be utilized to quickly and simply convert decimals to binary.
For example, you can employ the incorporated functions in a spreadsheet or a calculator program to convert decimals to binary. You can also utilize online tools such as binary converters, which allow you to enter a decimal number, and the converter will automatically generate the equivalent binary number.
It is important to note that the binary system has some constraints contrast to the decimal system.
For instance, the binary system is unable to portray fractions, so it is solely appropriate for dealing with whole numbers.
The binary system also needs more digits to illustrate 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 long string of 0s and 1s could be liable to typing errors and reading errors.
Final Thoughts on Decimal to Binary
Despite these restrictions, the binary system has several merits over the decimal system. For instance, the binary system is lot easier than the decimal system, as it only uses two digits. This simplicity makes it easier to perform mathematical operations in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is further suited to depict information in digital systems, such as computers, as it can simply be represented using electrical signals. As a consequence, knowledge of how to convert among the decimal and binary systems is important for computer programmers and for unraveling mathematical problems including huge numbers.
Even though the process of converting decimal to binary can be labor-intensive and vulnerable to errors when worked on manually, there are applications that can easily convert within the two systems.
