The decimal and binary number systems are the world’s most commonly 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 utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. However, the binary system, also known as the base-2 system, employees only two digits (0 and 1) to depict numbers.
Learning how to convert between the decimal and binary systems are essential for many reasons. For instance, computers use the binary system to portray data, so software programmers are supposed to be proficient in converting among the two systems.
Furthermore, understanding how to change within the two systems can helpful to solve math questions concerning enormous numbers.
This blog 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 procedure 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 prior step by 2, and document the quotient and the remainder.
Repeat the prior steps before the quotient is equivalent to 0.
The binary equal of the decimal number is acquired by reversing the sequence of the remainders obtained in the previous steps.
This may sound complicated, so here is an example to show you 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 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 conversion utilizing the steps 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 equivalent of 25 is 11001, that is gained 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, that is achieved by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described above provide a method to manually convert decimal to binary, it can be time-consuming and error-prone for big numbers. Luckily, other systems can be used to rapidly and simply change decimals to binary.
For instance, you can utilize the incorporated functions in a calculator or a spreadsheet application to convert decimals to binary. You can further utilize online tools such as binary converters, which allow you to enter a decimal number, and the converter will automatically generate the respective binary number.
It is worth noting that the binary system has few limitations compared to the decimal system.
For instance, the binary system fails to illustrate fractions, so it is only fit for dealing with whole numbers.
The binary system additionally requires more digits to illustrate a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The extended string of 0s and 1s can be liable to typing errors and reading errors.
Final Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has some advantages with the decimal system. For instance, the binary system is far simpler than the decimal system, as it just utilizes two digits. This simplicity makes it easier to perform mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more fitted to representing information in digital systems, such as computers, as it can simply be represented utilizing electrical signals. Consequently, knowledge of how to convert among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems including huge numbers.
While the process of changing decimal to binary can be tedious and prone with error when done manually, there are applications that can quickly convert among the two systems.
