The decimal and binary number systems are the world’s most frequently utilized number systems today.
The decimal system, also under the name of the base-10 system, is the system we utilize in our everyday 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.
Learning how to transform from and to the decimal and binary systems are vital for many reasons. For example, computers use the binary system to portray data, so computer engineers are supposed to be competent in converting between the two systems.
In addition, comprehending how to convert between the two systems can help solve mathematical questions involving large numbers.
This blog article will cover the formula for converting decimal to binary, provide a conversion chart, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of converting a decimal number to a binary number is performed manually utilizing the ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) collect in the last step by 2, and record the quotient and the remainder.
Reiterate the prior steps before the quotient is similar to 0.
The binary equal of the decimal number is obtained by reversing the series of the remainders obtained in the prior steps.
This may sound complicated, so here is an example to portray 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 gained 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 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 using 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, that is acquired 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 acquired by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps defined earlier offers a method to manually change decimal to binary, it can be time-consuming and error-prone for big numbers. Luckily, other systems can be utilized to rapidly and effortlessly change decimals to binary.
For example, you could utilize the built-in functions in a calculator or a spreadsheet program to change decimals to binary. You could further utilize online tools such as binary converters, which allow you to type a decimal number, and the converter will spontaneously generate the corresponding binary number.
It is important to note that the binary system has handful of limitations in comparison to the decimal system.
For example, the binary system fails to represent fractions, so it is solely fit for representing whole numbers.
The binary system also requires more digits to illustrate 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 extended string of 0s and 1s could be liable to typos and reading errors.
Concluding Thoughts on Decimal to Binary
Regardless these limitations, the binary system has a lot of merits with the decimal system. For instance, 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 instance addition, subtraction, multiplication, and division.
The binary system is further suited to depict information in digital systems, such as computers, as it can effortlessly be represented using electrical signals. As a result, understanding how to change among the decimal and binary systems is crucial for computer programmers and for solving mathematical problems involving huge numbers.
Even though the method of converting decimal to binary can be labor-intensive and prone with error when done manually, there are tools which can quickly convert among the two systems.
