The decimal and binary number systems are the world’s most frequently 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 utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. At the same time, the binary system, also called the base-2 system, utilizes only two digits (0 and 1) to represent numbers.
Comprehending how to convert between the decimal and binary systems are important for various reasons. For example, computers use the binary system to represent data, so software programmers should be expert in converting within the two systems.
In addition, learning how to change between the two systems can be beneficial to solve math questions including enormous numbers.
This article will cover the formula for converting decimal to binary, provide a conversion chart, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The procedure 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) found in the last step by 2, and record the quotient and the remainder.
Replicate the last steps until the quotient is equivalent to 0.
The binary corresponding of the decimal number is obtained by inverting the order of the remainders acquired in the previous steps.
This might sound complex, 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 reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table depicting the decimal and binary equals 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 instances of decimal to binary transformation 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 equal of 25 is 11001, that is obtained 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 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 earlier provide a way to manually convert decimal to binary, it can be time-consuming and open to error for large numbers. Fortunately, other ways can be used to quickly and effortlessly convert decimals to binary.
For example, you could utilize the built-in functions in a calculator or a spreadsheet application to change decimals to binary. You could also use online applications similar to binary converters, that enables you to input a decimal number, and the converter will automatically generate the respective binary number.
It is worth noting that the binary system has handful of limitations contrast to the decimal system.
For instance, the binary system cannot portray fractions, so it is solely fit for representing whole numbers.
The binary system additionally requires more digits to represent a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, that has six digits. The length string of 0s and 1s could be prone to typing errors and reading errors.
Final Thoughts on Decimal to Binary
Despite these restrictions, the binary system has some merits with the decimal system. For example, the binary system is far simpler than the decimal system, as it only utilizes two digits. This simplicity makes it simpler to conduct mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is further suited to depict information in digital systems, such as computers, as it can easily be portrayed using electrical signals. As a consequence, knowledge of how to transform among the decimal and binary systems is crucial for computer programmers and for solving mathematical questions involving huge numbers.
Although the process of changing decimal to binary can be tedious and prone with error when done manually, there are applications which can easily change between the two systems.
