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 use in our daily lives. It utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. On the other hand, the binary system, also called the base-2 system, employees only two figures (0 and 1) to portray numbers.
Learning how to convert between the decimal and binary systems are important for various reasons. For instance, computers utilize the binary system to represent data, so computer programmers should be proficient in changing between the two systems.
Additionally, comprehending how to convert among the two systems can help solve math problems including large numbers.
This blog article will go through the formula for changing decimal to binary, provide a conversion chart, and give instances 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 using the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) collect in the last step by 2, and note the quotient and the remainder.
Repeat the prior steps until the quotient is equal to 0.
The binary equal of the decimal number is achieved by reversing the series of the remainders received in the last steps.
This might sound confusing, so here is an example to show you 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 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 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 conversion employing the steps talked about priorly:
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 equivalent of 25 is 11001, that is gained by reversing the series 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, that is achieved by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described prior offers a way to manually change decimal to binary, it can be labor-intensive and error-prone for large numbers. Luckily, other ways can be utilized to quickly and effortlessly convert decimals to binary.
For instance, you can employ the built-in features in a calculator or a spreadsheet program to convert decimals to binary. You can further use web-based applications similar to binary converters, that allow you to input a decimal number, and the converter will spontaneously produce the equivalent binary number.
It is worth noting that the binary system has handful of limitations in comparison to the decimal system.
For instance, the binary system fails to illustrate fractions, so it is solely appropriate for representing whole numbers.
The binary system further needs 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 inclined to typos and reading errors.
Final Thoughts on Decimal to Binary
Regardless these limitations, 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 uses two digits. This simplicity makes it simpler to carry out mathematical functions in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is further fitted to representing information in digital systems, such as computers, as it can effortlessly be portrayed using electrical signals. As a consequence, understanding how to change between the decimal and binary systems is important for computer programmers and for solving mathematical problems including large numbers.
Even though the process of changing decimal to binary can be time-consuming and vulnerable to errors when done manually, there are tools that can quickly change between the two systems.
