The decimal and binary number systems are the world’s most commonly used number systems right now.
The decimal system, also known as the base-10 system, is the system we utilize in our daily lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. However, the binary system, also called the base-2 system, utilizes only two figures (0 and 1) to depict numbers.
Understanding how to transform from and to the decimal and binary systems are essential for many reasons. For instance, computers use the binary system to portray data, so computer engineers must be competent in converting between the two systems.
Additionally, learning how to change within the two systems can helpful to solve math problems including enormous numbers.
This article will cover the formula for converting decimal to binary, provide a conversion table, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The method of converting 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) collect in the last step by 2, and record the quotient and the remainder.
Replicate the previous steps before the quotient is equivalent to 0.
The binary corresponding of the decimal number is acquired by reversing the series of the remainders acquired in the last steps.
This might sound confusing, so here is an example to show you 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 equivalent 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 chart 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 few examples of decimal to binary transformation employing the steps talked about 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 equal 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 obtained by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps described earlier provide a method to manually convert decimal to binary, it can be tedious and error-prone for big numbers. Luckily, other systems can be utilized to swiftly and effortlessly change decimals to binary.
For instance, you could utilize the built-in features in a calculator or a spreadsheet program to convert decimals to binary. You can also use online applications such as binary converters, that enables you to enter a decimal number, and the converter will spontaneously generate the equivalent binary number.
It is worth noting that the binary system has few constraints compared to the decimal system.
For instance, the binary system fails to portray fractions, so it is solely appropriate for representing whole numbers.
The binary system also needs more digits to represent a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The extended string of 0s and 1s could be liable to typos and reading errors.
Final Thoughts on Decimal to Binary
Despite these limitations, the binary system has a lot of advantages over the decimal system. For example, the binary system is lot easier than the decimal system, as it only uses two digits. This simpleness makes it simpler to carry out mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is more suited to representing information in digital systems, such as computers, as it can easily be portrayed using electrical signals. As a result, understanding how to convert among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems concerning large numbers.
While the process of changing decimal to binary can be tedious and error-prone when done manually, there are applications that can easily change within the two systems.
