The decimal and binary number systems are the world’s most frequently used number systems today.
The decimal system, also known as 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 portray numbers. On the other hand, the binary system, also called the base-2 system, uses only two digits (0 and 1) to portray numbers.
Comprehending how to transform from and to the decimal and binary systems are important for multiple reasons. For example, computers utilize the binary system to depict data, so computer programmers must be expert in changing within the two systems.
Additionally, learning how to convert between the two systems can helpful to solve math questions including large numbers.
This article will go through the formula for transforming decimal to binary, offer 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 utilizing the ensuing steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) collect in the previous step by 2, and note the quotient and the remainder.
Repeat the last steps unless the quotient is equal to 0.
The binary equivalent of the decimal number is achieved by reversing the order of the remainders acquired in the prior steps.
This might sound complex, so here is an example to portray 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 equivalent 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 some examples of decimal to binary transformation using the method 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, which is acquired 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 obtained by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined above provide a way to manually convert decimal to binary, it can be labor-intensive and error-prone for large numbers. Luckily, other systems can be utilized to rapidly and easily convert decimals to binary.
For instance, you could utilize the incorporated functions in a spreadsheet or a calculator application to change decimals to binary. You could additionally utilize web-based tools such as binary converters, which allow you to type a decimal number, and the converter will spontaneously produce the corresponding binary number.
It is important to note that the binary system has few constraints in comparison to the decimal system.
For instance, the binary system is unable to represent fractions, so it is only fit for representing whole numbers.
The binary system additionally needs more digits to portray a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The length string of 0s and 1s can be prone to typos and reading errors.
Concluding Thoughts on Decimal to Binary
Regardless these limitations, the binary system has some advantages over 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 perform mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is further suited to depict information in digital systems, such as computers, as it can simply be depicted using electrical signals. As a result, understanding how to transform between the decimal and binary systems is important for computer programmers and for unraveling mathematical problems involving large numbers.
While the method of converting decimal to binary can be labor-intensive and error-prone when worked on manually, there are tools which can easily change between the two systems.
