The decimal and binary number systems are the world’s most frequently utilized number systems right now.
The decimal system, also known as the base-10 system, is the system we use in our daily lives. It utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. On the other hand, the binary system, also known as the base-2 system, employees only two digits (0 and 1) to portray numbers.
Understanding how to convert between the decimal and binary systems are essential for various reasons. For instance, computers use the binary system to portray data, so software engineers are supposed to be competent in converting among the two systems.
Furthermore, understanding how to change between the two systems can help solve math questions involving enormous numbers.
This blog article will go through the formula for converting decimal to binary, give a conversion table, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The process of changing a decimal number to a binary number is performed manually using the following steps:
Divide the decimal number by 2, and account 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 previous steps before the quotient is similar to 0.
The binary corresponding of the decimal number is acquired by reversing the sequence of the remainders acquired in the previous steps.
This may sound complicated, so here is an example to illustrate this process:
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 equal of 75 is 1001011, which is obtained by inverting 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 conversion employing the method discussed 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 equal of 25 is 11001, which is obtained 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, that is obtained by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined prior offers a way to manually change decimal to binary, it can be time-consuming and prone to error for big numbers. Fortunately, other methods can be employed to swiftly and effortlessly change decimals to binary.
For example, you can employ the built-in features in a spreadsheet or a calculator program to convert decimals to binary. You can further utilize online tools similar to binary converters, which allow you to enter a decimal number, and the converter will automatically produce the equivalent binary number.
It is worth pointing out that the binary system has few constraints in comparison to the decimal system.
For instance, the binary system cannot portray 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 instance, the decimal number 100 can be portrayed by the binary number 1100100, that has six digits. The long string of 0s and 1s could be inclined to typing errors and reading errors.
Last Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has a lot of advantages with the decimal system. For instance, the binary system is far simpler than the decimal system, as it just uses two digits. This simpleness makes it easier to carry out mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more fitted to representing information in digital systems, such as computers, as it can simply be portrayed using electrical signals. As a consequence, understanding how to convert among the decimal and binary systems is important for computer programmers and for unraveling mathematical problems involving large numbers.
While the method of changing decimal to binary can be tedious and vulnerable to errors when worked on manually, there are tools which can easily convert between the two systems.
