The decimal and binary number systems are the world’s most commonly utilized number systems presently.
The decimal system, also known as 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 illustrate numbers. On the other hand, the binary system, also known as the base-2 system, uses only two digits (0 and 1) to represent numbers.
Comprehending how to transform from and to the decimal and binary systems are essential for various reasons. For instance, computers use the binary system to depict data, so software engineers must be proficient in changing among the two systems.
Furthermore, learning how to convert within the two systems can helpful to solve math problems concerning enormous numbers.
This blog article will go through the formula for changing decimal to binary, offer a conversion chart, and give examples 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 previous step by 2, and note the quotient and the remainder.
Reiterate the previous steps until the quotient is equivalent to 0.
The binary equivalent of the decimal number is acquired by reversing the order of the remainders obtained in the last steps.
This might sound complex, 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 inverting 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 few examples of decimal to binary conversion utilizing the method talked about 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 series 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 equal of 128 is 10000000, that is obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined prior offers a method to manually convert decimal to binary, it can be time-consuming and error-prone for big numbers. Fortunately, other systems can be used to quickly and easily convert decimals to binary.
For instance, you could utilize the built-in functions in a spreadsheet or a calculator program to change decimals to binary. You could additionally utilize online tools for instance binary converters, that enables you to enter a decimal number, and the converter will spontaneously generate the corresponding binary number.
It is worth noting that the binary system has few limitations compared to the decimal system.
For example, the binary system cannot illustrate fractions, so it is only fit for representing whole numbers.
The binary system further needs more digits to portray 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 extended string of 0s and 1s could be prone to typos and reading errors.
Last Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has some advantages with the decimal system. For instance, the binary system is lot easier than the decimal system, as it only utilizes two digits. This simplicity makes it easier to conduct mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is more suited to representing information in digital systems, such as computers, as it can simply be portrayed utilizing electrical signals. As a result, understanding how to convert among the decimal and binary systems is essential for computer programmers and for solving mathematical questions involving huge numbers.
While the method of converting decimal to binary can be tedious and vulnerable to errors when worked on manually, there are tools which can rapidly change among the two systems.
