The decimal and binary number systems are the world’s most frequently used number systems right now.
The decimal system, also called the base-10 system, is the system we utilize in our everyday lives. It uses ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. However, the binary system, also called the base-2 system, uses only two figures (0 and 1) to represent numbers.
Comprehending how to transform from and to the decimal and binary systems are important for various 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.
Additionally, understanding how to convert within the two systems can help solve math problems concerning enormous numbers.
This blog will cover the formula for changing decimal to binary, provide a conversion table, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The process of transforming a decimal number to a binary number is done manually using the following steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) collect in the previous step by 2, and record the quotient and the remainder.
Reiterate the last steps until the quotient is equivalent to 0.
The binary corresponding of the decimal number is achieved by reversing the sequence of the remainders received in the last steps.
This may sound confusing, so here is an example to illustrate this method:
Let’s convert 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 acquired by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table depicting 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 few instances of decimal to binary conversion employing the method discussed earlier:
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, which is gained 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 equivalent of 128 is 10000000, that is obtained by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps described above provide a method to manually change decimal to binary, it can be labor-intensive and open to error for big numbers. Thankfully, other systems can be used to swiftly and effortlessly change decimals to binary.
For example, you could use the incorporated features in a calculator or a spreadsheet program to change decimals to binary. You could additionally utilize web-based tools for instance binary converters, which allow you to type a decimal number, and the converter will automatically generate the corresponding binary number.
It is important to note that the binary system has few limitations compared to the decimal system.
For instance, the binary system cannot represent fractions, so it is solely suitable for representing whole numbers.
The binary system additionally requires more digits to portray a number than the decimal system. For instance, the decimal number 100 can be represented by the binary number 1100100, that has six digits. The long string of 0s and 1s could be liable to typos and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these limitations, the binary system has several 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 suited to depict information in digital systems, such as computers, as it can easily be depicted using electrical signals. Consequently, knowledge of how to change among the decimal and binary systems is important for computer programmers and for unraveling mathematical problems concerning huge numbers.
Even though the process of converting decimal to binary can be tedious and vulnerable to errors when done manually, there are applications that can easily change within the two systems.
