The decimal and binary number systems are the world’s most commonly 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 represent numbers. However, the binary system, also known as the base-2 system, uses only two figures (0 and 1) to portray numbers.
Comprehending how to transform from and to the decimal and binary systems are important for various reasons. For instance, computers utilize the binary system to portray data, so software engineers must be competent in changing within the two systems.
Additionally, comprehending how to convert among the two systems can helpful to solve math questions including enormous numbers.
This blog will go through the formula for transforming decimal to binary, give a conversion chart, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The process of changing a decimal number to a binary number is done manually using the following steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) obtained in the prior step by 2, and record 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 inverting the order of the remainders obtained in the prior steps.
This might sound complex, so here is an example to show you 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 equivalent 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 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 few examples of decimal to binary transformation employing the method talked about 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, which is acquired 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, which is acquired by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps defined above offers a way to manually convert decimal to binary, it can be labor-intensive and prone to error for large numbers. Fortunately, other methods can be used to swiftly and simply change decimals to binary.
For instance, you could employ the incorporated features in a calculator or a spreadsheet application to convert decimals to binary. You can also use online tools similar to binary converters, that enables you to type a decimal number, and the converter will spontaneously generate the equivalent binary number.
It is important to note that the binary system has few constraints in comparison to the decimal system.
For example, the binary system is unable to represent fractions, so it is only fit for representing whole numbers.
The binary system also needs more digits to illustrate a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The long string of 0s and 1s could be liable to typos and reading errors.
Last Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has some advantages with the decimal system. For example, the binary system is far simpler than the decimal system, as it only uses two digits. This simpleness 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 representing information in digital systems, such as computers, as it can effortlessly be portrayed using electrical signals. Consequently, understanding how to transform between the decimal and binary systems is crucial for computer programmers and for unraveling mathematical questions including large numbers.
Even though the method of converting decimal to binary can be tedious and error-prone when done manually, there are tools which can rapidly convert among the two systems.
