The decimal and binary number systems are the world’s most frequently utilized number systems presently.
The decimal system, also called the base-10 system, is the system we use in our everyday lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. At the same time, the binary system, also called the base-2 system, employees only two digits (0 and 1) to portray numbers.
Comprehending how to convert between the decimal and binary systems are essential for many reasons. For instance, computers utilize the binary system to portray data, so software programmers are supposed to be proficient in changing among the two systems.
In addition, learning how to convert within the two systems can help solve mathematical problems involving large numbers.
This blog will cover the formula for changing decimal to binary, offer a conversion table, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of converting a decimal number to a binary number is done 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 last step by 2, and note the quotient and the remainder.
Reiterate the previous steps until the quotient is similar to 0.
The binary equivalent of the decimal number is acquired by inverting the order of the remainders received in the prior steps.
This may sound confusing, so here is an example to portray 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 table showing 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 conversion using the method discussed priorly:
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: 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 equivalent of 128 is 10000000, which is obtained by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined above provide a way to manually convert decimal to binary, it can be labor-intensive and open to error for large numbers. Thankfully, other ways can be employed to rapidly and effortlessly convert decimals to binary.
For instance, you can use the incorporated functions in a spreadsheet or a calculator program to change decimals to binary. You can additionally use web tools for instance binary converters, that enables you to type a decimal number, and the converter will spontaneously generate the respective binary number.
It is important to note that the binary system has handful of limitations compared to the decimal system.
For example, the binary system is unable to illustrate fractions, so it is solely appropriate for dealing with whole numbers.
The binary system also requires more digits to illustrate a number than the decimal system. For example, the decimal number 100 can be portrayed by the binary number 1100100, that has six digits. The extended string of 0s and 1s could be liable to typos and reading errors.
Last Thoughts on Decimal to Binary
Despite these restrictions, the binary system has several advantages over the decimal system. For instance, the binary system is far simpler than the decimal system, as it just uses two digits. This simplicity makes it easier to carry out mathematical operations in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is more fitted to depict information in digital systems, such as computers, as it can easily be portrayed using electrical signals. As a result, knowledge of how to convert between the decimal and binary systems is important for computer programmers and for unraveling mathematical problems including huge numbers.
Even though the process of converting decimal to binary can be time-consuming and prone with error when worked on manually, there are applications that can rapidly convert between the two systems.
