The decimal and binary number systems are the world’s most commonly utilized number systems right now.
The decimal system, also under the name of the base-10 system, is the system we utilize in our daily lives. It uses ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. However, the binary system, also called the base-2 system, employees only two digits (0 and 1) to depict numbers.
Comprehending how to convert between the decimal and binary systems are important for various reasons. For instance, computers use the binary system to depict data, so computer engineers are supposed to be proficient in changing within the two systems.
Furthermore, understanding how to change among the two systems can be beneficial to solve math questions including large numbers.
This article will go through the formula for transforming decimal to binary, give a conversion chart, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The method of changing a decimal number to a binary number is performed manually using the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) obtained in the previous step by 2, and note the quotient and the remainder.
Replicate the last steps before the quotient is equal to 0.
The binary equivalent of the decimal number is acquired by inverting the sequence of the remainders received in the previous steps.
This might sound complex, so here is an example to illustrate 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 gained by inverting the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table depicting 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 instances of decimal to binary transformation utilizing the method discussed 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, 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 equivalent of 128 is 10000000, that is obtained by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps defined above offers a method to manually change decimal to binary, it can be labor-intensive and open to error for large numbers. Thankfully, other ways can be employed to quickly and effortlessly change decimals to binary.
For example, you could employ the incorporated functions in a calculator or a spreadsheet application to convert decimals to binary. You could also use online tools such as binary converters, that allow you to type a decimal number, and the converter will automatically produce the respective binary number.
It is worth noting that the binary system has few limitations contrast to the decimal system.
For example, the binary system cannot portray fractions, so it is only appropriate for representing whole numbers.
The binary system also needs 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 liable to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Regardless these limitations, the binary system has some 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 simpler to carry out mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is more fitted to depict information in digital systems, such as computers, as it can simply be represented utilizing electrical signals. Consequently, understanding how to convert among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems concerning large numbers.
Although the process of converting decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are applications that can easily change between the two systems.
