The decimal and binary number systems are the world’s most frequently used number systems presently.
The decimal system, also called 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 portray numbers. However, 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 many reasons. For example, computers use the binary system to depict data, so computer programmers must be expert in converting between the two systems.
Additionally, understanding how to change between the two systems can helpful to solve math questions concerning large numbers.
This article will go through the formula for converting decimal to binary, provide a conversion chart, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The procedure of converting a decimal number to a binary number is done manually using the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) obtained in the last step by 2, and note the quotient and the remainder.
Reiterate the previous steps unless the quotient is similar to 0.
The binary equal 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 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 acquired by inverting the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart portraying 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 conversion employing the steps discussed 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 series 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).
While the steps defined earlier provide a way to manually change decimal to binary, it can be tedious and open to error for large numbers. Thankfully, other ways can be used to quickly and effortlessly convert decimals to binary.
For instance, you could utilize the built-in functions in a spreadsheet or a calculator program to convert decimals to binary. You could further utilize web tools such as binary converters, that enables you to enter a decimal number, and the converter will spontaneously produce the corresponding binary number.
It is worth pointing out that the binary system has few limitations compared to the decimal system.
For example, the binary system fails to represent fractions, so it is only appropriate for representing whole numbers.
The binary system also requires more digits to portray a number than the decimal system. For example, the decimal number 100 can be represented by the binary number 1100100, which has six digits. The long string of 0s and 1s could be liable to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Despite these limits, the binary system has some merits with the decimal system. For example, the binary system is lot easier than the decimal system, as it only utilizes two digits. This simplicity makes it easier to carry out mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is further suited to representing information in digital systems, such as computers, as it can effortlessly be depicted using electrical signals. As a result, understanding how to change between the decimal and binary systems is essential for computer programmers and for unraveling mathematical questions concerning huge numbers.
While the process of converting decimal to binary can be tedious and vulnerable to errors when worked on manually, there are applications that can easily change between the two systems.
