The decimal and binary number systems are the world’s most commonly utilized number systems presently.
The decimal system, also called the base-10 system, is the system we use in our everyday lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. On the other hand, the binary system, also called the base-2 system, employees only two digits (0 and 1) to represent numbers.
Understanding how to convert between the decimal and binary systems are vital for many reasons. For instance, computers use the binary system to portray data, so software programmers should be expert in changing within the two systems.
Furthermore, learning how to change within the two systems can help solve mathematical problems including large numbers.
This blog article will cover the formula for transforming decimal to binary, provide a conversion chart, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The method of transforming a decimal number to a binary number is performed manually utilizing the following steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) collect in the prior step by 2, and document the quotient and the remainder.
Reiterate the prior steps unless the quotient is similar to 0.
The binary equal of the decimal number is acquired by reversing the sequence of the remainders received in the previous steps.
This may sound complex, 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 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 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 conversion employing the method discussed 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, which is obtained by inverting the series 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 achieved by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined earlier provide a method to manually convert decimal to binary, it can be labor-intensive and error-prone for large numbers. Fortunately, other systems can be used to quickly and simply convert decimals to binary.
For instance, you could use the built-in functions in a spreadsheet or a calculator program to change decimals to binary. You could further utilize web-based tools such as binary converters, that enables you to type a decimal number, and the converter will automatically produce the equivalent binary number.
It is important to note that the binary system has few constraints contrast to the decimal system.
For example, the binary system cannot illustrate fractions, so it is solely fit for representing whole numbers.
The binary system also requires more digits to represent a number than the decimal system. For example, the decimal number 100 can be represented by the binary number 1100100, that has six digits. The long string of 0s and 1s could be inclined to typos and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these limits, the binary system has some advantages with the decimal system. For example, the binary system is far simpler than the decimal system, as it just uses two digits. This simpleness makes it simpler to conduct mathematical functions 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 using electrical signals. As a consequence, understanding how to convert between the decimal and binary systems is important for computer programmers and for solving mathematical problems including huge numbers.
Even though the process of converting decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are tools which can quickly change within the two systems.
