The decimal and binary number systems are the world’s most frequently utilized number systems presently.
The decimal system, also under the name of the base-10 system, is the system we utilize in our everyday lives. It utilizes ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. However, the binary system, also called the base-2 system, uses only two digits (0 and 1) to portray numbers.
Comprehending how to transform from and to the decimal and binary systems are vital for many reasons. For instance, computers utilize the binary system to depict data, so computer engineers are supposed to be proficient in converting among the two systems.
Furthermore, understanding how to change among the two systems can be beneficial to solve math problems including large numbers.
This article will go through the formula for converting decimal to binary, offer a conversion table, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The procedure of converting a decimal number to a binary number is performed manually utilizing the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) collect in the last step by 2, and note the quotient and the remainder.
Repeat the previous steps until the quotient is similar to 0.
The binary corresponding of the decimal number is acquired by reversing the order of the remainders received in the previous steps.
This might sound complex, so here is an example to show you this process:
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 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 few 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 equal of 25 is 11001, which is obtained 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, that is obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps defined earlier provide a method to manually convert decimal to binary, it can be time-consuming and prone to error for large numbers. Thankfully, other methods can be used to quickly and simply change decimals to binary.
For instance, you can employ the incorporated features in a spreadsheet or a calculator program to convert decimals to binary. You could also utilize web tools for instance binary converters, which allow you to type a decimal number, and the converter will spontaneously generate the corresponding binary number.
It is worth noting that the binary system has handful of constraints compared to the decimal system.
For instance, the binary system is unable to portray fractions, so it is only fit for representing whole numbers.
The binary system also requires more digits to represent 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 could be prone to typos and reading errors.
Final Thoughts on Decimal to Binary
Despite these limits, the binary system has some merits over the decimal system. For example, the binary system is far simpler than the decimal system, as it only utilizes two digits. This simpleness makes it simpler to conduct mathematical operations in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is more suited to depict information in digital systems, such as computers, as it can easily be portrayed using electrical signals. Consequently, knowledge of how to transform between the decimal and binary systems is essential for computer programmers and for unraveling mathematical questions including large numbers.
While the method of changing decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are applications which can rapidly change within the two systems.
