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 utilizes ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. However, the binary system, also known as the base-2 system, utilizes only two figures (0 and 1) to portray numbers.
Comprehending how to convert between the decimal and binary systems are vital for multiple reasons. For instance, computers use the binary system to portray data, so computer engineers must be expert in converting within the two systems.
Furthermore, understanding how to change among the two systems can be beneficial to solve mathematical questions concerning enormous numbers.
This blog will cover the formula for changing decimal to binary, provide a conversion table, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The procedure of changing a decimal number to a binary number is performed manually utilizing the ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) found in the previous step by 2, and note the quotient and the remainder.
Repeat the prior steps before the quotient is similar to 0.
The binary equal of the decimal number is acquired by reversing the series of the remainders acquired in the previous steps.
This may sound confusing, 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 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 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 some instances of decimal to binary conversion 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 equal of 25 is 11001, which is acquired by inverting 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, which is achieved by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described earlier provide a way to manually change decimal to binary, it can be labor-intensive and error-prone for big numbers. Fortunately, other ways can be used to swiftly and easily convert decimals to binary.
For example, you could utilize the built-in features in a spreadsheet or a calculator program to convert decimals to binary. You can further utilize online applications such as binary converters, that allow you to input a decimal number, and the converter will spontaneously generate the respective binary number.
It is worth pointing out that the binary system has few constraints contrast to the decimal system.
For instance, the binary system is unable to illustrate fractions, so it is only fit for representing 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 extended string of 0s and 1s could be prone to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has a lot of merits with the decimal system. For example, the binary system is much simpler than the decimal system, as it only uses two digits. This simplicity makes it easier to carry out mathematical functions in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more fitted to depict information in digital systems, such as computers, as it can effortlessly be represented utilizing electrical signals. Consequently, knowledge of how to change among the decimal and binary systems is important for computer programmers and for solving mathematical problems including huge numbers.
Even though the method of changing decimal to binary can be tedious and vulnerable to errors when done manually, there are applications that can rapidly change within the two systems.
