The decimal and binary number systems are the world’s most frequently utilized number systems presently.
The decimal system, also under the name of the base-10 system, is the system we utilize in our daily lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. At the same time, the binary system, also called the base-2 system, utilizes only two digits (0 and 1) to depict numbers.
Understanding how to convert between the decimal and binary systems are vital for many reasons. For instance, computers use the binary system to represent data, so computer programmers are supposed to be competent in changing within the two systems.
Furthermore, comprehending how to change within the two systems can be beneficial to solve math questions concerning enormous numbers.
This blog article will cover the formula for changing decimal to binary, provide a conversion chart, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of transforming a decimal number to a binary number is performed 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 document the quotient and the remainder.
Reiterate the previous steps before the quotient is equal to 0.
The binary corresponding of the decimal number is acquired by reversing the sequence of the remainders received in the prior steps.
This may sound confusing, 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 equal 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 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 some examples of decimal to binary conversion utilizing the steps talked about priorly:
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 equivalent of 25 is 11001, that is obtained 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 equal of 128 is 10000000, that is achieved by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined above provide a method to manually change decimal to binary, it can be tedious and open to error for big numbers. Luckily, other systems can be used to rapidly and easily change decimals to binary.
For example, you can use the built-in functions in a spreadsheet or a calculator program to change decimals to binary. You can also use online applications for instance binary converters, which allow you to input a decimal number, and the converter will spontaneously generate the corresponding binary number.
It is worth noting that the binary system has few limitations in comparison to the decimal system.
For instance, the binary system is unable to represent fractions, so it is solely suitable for dealing with whole numbers.
The binary system further requires more digits to illustrate 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 long string of 0s and 1s can be prone to typos and reading errors.
Final Thoughts on Decimal to Binary
In spite of these limits, the binary system has several advantages with the decimal system. For example, the binary system is lot easier than the decimal system, as it only uses two digits. This simpleness makes it easier to carry out mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is more suited to depict information in digital systems, such as computers, as it can simply be depicted 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 involving huge numbers.
Even though the method of changing decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are applications that can rapidly convert within the two systems.
