The decimal and binary number systems are the world’s most commonly used number systems presently.
The decimal system, also under the name of the base-10 system, is the system we utilize in our everyday lives. It utilizes 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, uses only two digits (0 and 1) to represent numbers.
Understanding how to transform from and to the decimal and binary systems are important for multiple reasons. For instance, computers use the binary system to represent data, so software engineers must be competent in converting among the two systems.
Additionally, learning how to convert between the two systems can be beneficial to solve math problems including enormous numbers.
This article will go through the formula for converting decimal to binary, give a conversion table, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of transforming a decimal number to a binary number is performed manually using the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) found in the prior step by 2, and document the quotient and the remainder.
Reiterate the previous steps before the quotient is equal to 0.
The binary equal of the decimal number is obtained by reversing the order of the remainders obtained in the previous steps.
This may sound complicated, so here is an example to show you 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 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 table 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 transformation using the steps talked about 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 equal of 128 is 10000000, which is acquired by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps described prior offers a method to manually change decimal to binary, it can be tedious and open to error for large numbers. Thankfully, other ways can be utilized to swiftly and effortlessly convert decimals to binary.
For instance, you could employ the built-in functions in a spreadsheet or a calculator application to change decimals to binary. You can additionally use web tools such as binary converters, that allow you to type a decimal number, and the converter will automatically produce the corresponding binary number.
It is worth pointing out that the binary system has some constraints compared to the decimal system.
For example, the binary system is unable to illustrate fractions, so it is solely fit for dealing with 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 portrayed by the binary number 1100100, that has six digits. The long string of 0s and 1s could be prone to typing errors and reading errors.
Final Thoughts on Decimal to Binary
In spite of these limitations, the binary system has some merits with the decimal system. For instance, the binary system is lot easier than the decimal system, as it only uses two digits. This simpleness makes it simpler 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 represented utilizing electrical signals. As a result, understanding how to convert between the decimal and binary systems is crucial for computer programmers and for solving mathematical questions involving large numbers.
While the method of changing decimal to binary can be labor-intensive and prone with error when worked on manually, there are tools that can easily convert among the two systems.
