The decimal and binary number systems are the world’s most frequently utilized number systems today.
The decimal system, also known as the base-10 system, is the system we use in our daily lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. On the other hand, the binary system, also known as the base-2 system, employees only two digits (0 and 1) to portray 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 must be proficient in converting between the two systems.
In addition, understanding how to change among the two systems can help solve math questions including large numbers.
This blog will go through 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 process of transforming a decimal number to a binary number is done manually utilizing the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) obtained in the previous step by 2, and document the quotient and the remainder.
Reiterate the prior steps unless the quotient is equal to 0.
The binary equivalent of the decimal number is achieved by inverting the series of the remainders obtained in the previous steps.
This may sound complicated, so here is an example to portray 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 acquired by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart 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 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, which 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 equivalent of 128 is 10000000, which is acquired by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps defined earlier offers a way to manually convert decimal to binary, it can be time-consuming and error-prone for large numbers. Luckily, other ways can be used to quickly and effortlessly change decimals to binary.
For example, you could utilize the incorporated functions in a spreadsheet or a calculator application to convert decimals to binary. You could further use web tools for instance binary converters, that allow you to enter a decimal number, and the converter will automatically produce the respective binary number.
It is worth pointing out that the binary system has handful of constraints contrast to the decimal system.
For instance, the binary system cannot illustrate fractions, so it is solely fit for representing whole numbers.
The binary system additionally requires more digits to portray a number than the decimal system. For instance, the decimal number 100 can be portrayed by the binary number 1100100, which has six digits. The extended string of 0s and 1s can be prone to typos and reading errors.
Last Thoughts on Decimal to Binary
Despite these limits, the binary system has several advantages over the decimal system. For example, the binary system is lot easier than the decimal system, as it just uses two digits. This simpleness makes it easier to perform mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is further suited to representing information in digital systems, such as computers, as it can easily be portrayed using electrical signals. Consequently, knowledge of how to transform among the decimal and binary systems is important for computer programmers and for unraveling mathematical problems involving huge numbers.
Even though the method of converting decimal to binary can be labor-intensive and error-prone when worked on manually, there are tools that can quickly change among the two systems.
