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 use in our daily lives. It employees ten figures (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 portray numbers.
Comprehending how to transform from and to the decimal and binary systems are vital for many reasons. For instance, computers utilize the binary system to depict data, so software programmers must be proficient in converting between the two systems.
Additionally, comprehending how to convert between the two systems can help solve math questions involving large numbers.
This blog article will go through the formula for transforming decimal to binary, offer a conversion chart, 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 done manually utilizing the ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) collect in the last step by 2, and document the quotient and the remainder.
Replicate the last steps unless the quotient is similar to 0.
The binary equivalent of the decimal number is obtained by inverting the order of the remainders obtained in the previous steps.
This might sound complicated, 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 obtained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table showing 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 examples of decimal to binary transformation utilizing the steps 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, that 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 equal of 128 is 10000000, which is achieved by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined earlier offers a way to manually change decimal to binary, it can be labor-intensive and prone to error for large numbers. Thankfully, other systems can be used to rapidly and easily convert decimals to binary.
For instance, you can utilize the incorporated features in a spreadsheet or a calculator program to convert decimals to binary. You could also use web-based tools such as binary converters, that enables you to enter a decimal number, and the converter will automatically generate the respective binary number.
It is important to note that the binary system has handful of constraints contrast to the decimal system.
For example, the binary system fails to illustrate fractions, so it is solely appropriate for representing whole numbers.
The binary system also needs more digits to represent a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, that 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
Despite these limitations, the binary system has several merits with the decimal system. For instance, the binary system is much simpler than the decimal system, as it only utilizes two digits. This simplicity makes it easier to conduct mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more suited to representing information in digital systems, such as computers, as it can effortlessly be depicted utilizing electrical signals. Consequently, understanding how to change between the decimal and binary systems is crucial for computer programmers and for solving mathematical problems involving huge numbers.
Although the process of changing decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are applications that can quickly convert among the two systems.
