The decimal and binary number systems are the world’s most commonly utilized number systems today.
The decimal system, also called 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 represent numbers. However, the binary system, also called the base-2 system, uses only two digits (0 and 1) to represent numbers.
Understanding how to transform from and to the decimal and binary systems are vital for many reasons. For instance, computers use the binary system to depict data, so software programmers are supposed to be expert in converting within the two systems.
In addition, comprehending how to change within the two systems can be beneficial to solve math questions concerning large numbers.
This article will go through the formula for converting decimal to binary, offer a conversion chart, 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 record the quotient and the remainder.
Divide the quotient (only) obtained in the previous step by 2, and record the quotient and the remainder.
Replicate the last steps until the quotient is equal to 0.
The binary corresponding of the decimal number is acquired by inverting the sequence of the remainders acquired in the prior steps.
This may sound complex, so here is an example to portray 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 portraying 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 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 equivalent 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 equivalent of 128 is 10000000, which is obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps outlined earlier offers a way to manually convert decimal to binary, it can be time-consuming and error-prone for big numbers. Luckily, other systems can be utilized to quickly and effortlessly change decimals to binary.
For instance, you could use the built-in functions in a spreadsheet or a calculator application to convert decimals to binary. You could further use web-based applications for instance binary converters, that enables you to enter a decimal number, and the converter will automatically generate the corresponding binary number.
It is worth pointing out that the binary system has handful of limitations compared to the decimal system.
For example, the binary system cannot portray fractions, so it is only suitable for dealing with whole numbers.
The binary system further needs more digits to illustrate 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 liable to typos and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has several merits with the decimal system. For example, the binary system is much simpler than the decimal system, as it just utilizes two digits. This simpleness makes it simpler to perform mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more fitted to representing information in digital systems, such as computers, as it can effortlessly be depicted utilizing electrical signals. Consequently, understanding how to change between the decimal and binary systems is crucial for computer programmers and for solving mathematical problems concerning large numbers.
While the process of converting decimal to binary can be time-consuming and vulnerable to errors when done manually, there are applications which can easily change among the two systems.
