The decimal and binary number systems are the world’s most commonly used number systems right now.
The decimal system, also called the base-10 system, is the system we utilize in our daily lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. However, the binary system, also known as the base-2 system, utilizes only two digits (0 and 1) to represent numbers.
Learning how to transform from and to the decimal and binary systems are vital for multiple reasons. For example, computers utilize the binary system to portray data, so computer engineers should be expert in converting within the two systems.
Furthermore, understanding how to convert between the two systems can be beneficial to solve math questions including large numbers.
This article will go through the formula for changing decimal to binary, offer a conversion table, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The process of converting a decimal number to a binary number is done 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 prior step by 2, and document the quotient and the remainder.
Replicate the prior steps unless the quotient is equal to 0.
The binary equivalent of the decimal number is obtained by inverting the sequence of the remainders acquired in the last steps.
This may sound complex, 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 gained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table 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 some instances of decimal to binary conversion using the steps talked about earlier:
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, that is acquired 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 obtained by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps defined above provide a method to manually change decimal to binary, it can be tedious and open to error for big numbers. Thankfully, other systems can be utilized to rapidly and easily convert decimals to binary.
For example, you could use the incorporated features in a spreadsheet or a calculator application to change decimals to binary. You could also use web-based applications similar to binary converters, which enables you to enter a decimal number, and the converter will spontaneously produce the corresponding binary number.
It is worth pointing out that the binary system has some limitations in comparison to the decimal system.
For instance, the binary system fails to illustrate fractions, so it is solely suitable for dealing with whole numbers.
The binary system also needs more digits to represent a number than the decimal system. For instance, the decimal number 100 can be illustrated by the binary number 1100100, that has six digits. The long 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 merits with 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 conduct mathematical operations in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further suited to representing information in digital systems, such as computers, as it can simply be portrayed utilizing electrical signals. As a consequence, knowledge of how to convert among the decimal and binary systems is crucial for computer programmers and for solving mathematical problems involving huge numbers.
While the method of changing decimal to binary can be tedious and prone with error when done manually, there are applications which can rapidly convert between the two systems.
