The decimal and binary number systems are the world’s most commonly used number systems presently.
The decimal system, also known as the base-10 system, is the system we use in our daily lives. It uses ten digits (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, employees only two figures (0 and 1) to represent numbers.
Learning how to transform from and to the decimal and binary systems are essential for various reasons. For instance, computers utilize the binary system to portray data, so software engineers must be proficient in changing within the two systems.
Furthermore, comprehending how to change within the two systems can be beneficial to solve mathematical questions including enormous numbers.
This article will cover the formula for converting decimal to binary, give a conversion chart, and give examples 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 following steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) found in the previous step by 2, and note the quotient and the remainder.
Reiterate the previous steps until the quotient is equivalent to 0.
The binary corresponding of the decimal number is acquired by reversing the series of the remainders received in the last steps.
This might 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 equivalent 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 table portraying the decimal and binary equivalents 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 conversion utilizing 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 equivalent of 25 is 11001, that is acquired by reversing 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 equivalent of 128 is 10000000, that is achieved by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps defined earlier provide a way to manually change decimal to binary, it can be time-consuming and open to error for large numbers. Thankfully, other ways can be utilized to quickly and effortlessly convert decimals to binary.
For example, you can use the incorporated functions in a calculator or a spreadsheet program to change decimals to binary. You could additionally utilize online applications for instance 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 in comparison to the decimal system.
For instance, the binary system cannot portray fractions, so it is solely fit for representing whole numbers.
The binary system additionally requires more digits to illustrate 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 can be inclined to typos and reading errors.
Last Thoughts on Decimal to Binary
In spite of these limitations, the binary system has some advantages with the decimal system. For example, the binary system is far simpler than the decimal system, as it just utilizes 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 easily be represented using electrical signals. As a result, understanding how to convert between the decimal and binary systems is crucial for computer programmers and for unraveling mathematical questions involving large numbers.
While the process of changing decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are tools that can easily convert between the two systems.
