The decimal and binary number systems are the world’s most frequently utilized number systems presently.
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 represent numbers. However, the binary system, also known as the base-2 system, utilizes only two figures (0 and 1) to portray numbers.
Learning how to convert between the decimal and binary systems are essential for multiple reasons. For instance, computers use the binary system to depict data, so software programmers are supposed to be proficient in changing within the two systems.
Additionally, comprehending how to change between the two systems can helpful to solve math questions involving 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 Changing Decimal to Binary
The process of changing a decimal number to a binary number is performed manually utilizing the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) obtained in the prior step by 2, and record the quotient and the remainder.
Repeat the previous steps until the quotient is similar to 0.
The binary corresponding of the decimal number is acquired by reversing the series of the remainders acquired in the prior steps.
This may sound complicated, so here is an example to show you 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 depicting 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 method 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 equal of 25 is 11001, that is gained by inverting the sequence 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, which is acquired by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps defined earlier provide a method to manually change decimal to binary, it can be tedious and prone to error for large numbers. Thankfully, other methods can be used to rapidly and effortlessly convert decimals to binary.
For example, you could utilize the built-in functions in a spreadsheet or a calculator application to change decimals to binary. You can further use web-based tools such as binary converters, which allow you to type a decimal number, and the converter will automatically generate the corresponding binary number.
It is worth noting that the binary system has handful of limitations compared to the decimal system.
For example, the binary system cannot represent fractions, so it is only fit for representing whole numbers.
The binary system also requires more digits to illustrate a number than the decimal system. For instance, the decimal number 100 can be represented by the binary number 1100100, that has six digits. The extended string of 0s and 1s can be prone to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has several advantages with the decimal system. For example, the binary system is far simpler than the decimal system, as it only uses two digits. This simpleness makes it simpler to carry out mathematical functions 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 effortlessly be represented using electrical signals. As a result, knowledge of how to transform between the decimal and binary systems is important for computer programmers and for unraveling mathematical problems involving huge numbers.
Even though the method of changing decimal to binary can be labor-intensive and prone with error when worked on manually, there are applications which can rapidly change between the two systems.
