The decimal and binary number systems are the world’s most frequently utilized number systems today.
The decimal system, also under the name of the base-10 system, is the system we use in our everyday lives. It utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. However, the binary system, also known as the base-2 system, utilizes only two figures (0 and 1) to depict numbers.
Learning how to transform from and to the decimal and binary systems are vital for various reasons. For instance, computers utilize the binary system to depict data, so software engineers are supposed to be proficient in converting within the two systems.
Furthermore, learning how to change between the two systems can be beneficial to solve mathematical problems involving large numbers.
This article will cover the formula for transforming decimal to binary, give a conversion table, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The procedure of changing a decimal number to a binary number is performed manually using the ensuing steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) found in the last step by 2, and document the quotient and the remainder.
Replicate the prior steps unless the quotient is equivalent to 0.
The binary corresponding of the decimal number is obtained by reversing the series of the remainders acquired in the prior steps.
This might sound confusing, so here is an example to illustrate 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 gained 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 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 examples of decimal to binary transformation using the steps 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 equivalent of 25 is 11001, which is gained 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 equal of 128 is 10000000, that is acquired by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps described prior provide a method to manually convert decimal to binary, it can be labor-intensive and prone to error for big numbers. Luckily, other ways can be employed to quickly and easily change decimals to binary.
For instance, you could use the incorporated functions in a spreadsheet or a calculator program to change decimals to binary. You can additionally utilize online applications such as binary converters, which allow you to enter a decimal number, and the converter will automatically generate the respective binary number.
It is important to note that the binary system has few constraints compared to the decimal system.
For example, the binary system is unable to represent fractions, so it is solely appropriate for representing whole numbers.
The binary system further needs more digits to represent a number than the decimal system. For instance, the decimal number 100 can be portrayed by the binary number 1100100, that has six digits. The long string of 0s and 1s could be inclined to typos and reading errors.
Final Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has several merits with the decimal system. For instance, the binary system is much simpler than the decimal system, as it only utilizes two digits. This simplicity makes it easier to perform mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is further fitted to depict information in digital systems, such as computers, as it can easily be depicted using electrical signals. As a result, understanding how to change between the decimal and binary systems is important for computer programmers and for unraveling mathematical questions involving huge numbers.
Even though the process of changing decimal to binary can be tedious and error-prone when worked on manually, there are tools which can rapidly convert within the two systems.
