The decimal and binary number systems are the world’s most commonly used number systems today.
The decimal system, also known as 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 represent numbers. At the same time, the binary system, also called the base-2 system, uses only two figures (0 and 1) to depict numbers.
Comprehending how to convert between the decimal and binary systems are essential for multiple reasons. For instance, computers use the binary system to depict data, so software programmers are supposed to be expert in changing between the two systems.
Furthermore, learning how to convert between the two systems can help solve mathematical problems including large numbers.
This blog article will cover the formula for changing decimal to binary, give a conversion chart, and give examples 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 ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) found in the previous step by 2, and note the quotient and the remainder.
Reiterate the last steps unless the quotient is equal to 0.
The binary corresponding of the decimal number is achieved by reversing the series of the remainders received in the previous steps.
This may sound complicated, so here is an example to portray this process:
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 equal of 75 is 1001011, which is acquired by inverting 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 few instances of decimal to binary conversion employing 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 inverting the sequence of remainders (1, 1, 0, 0, 1).
Example 2: Convert 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, that is achieved by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps described above provide a way to manually convert decimal to binary, it can be tedious and error-prone for large numbers. Thankfully, other systems can be used to swiftly and easily change decimals to binary.
For example, you can use the incorporated features in a spreadsheet or a calculator application to change decimals to binary. You could further utilize web applications similar to binary converters, which enables you to type a decimal number, and the converter will spontaneously generate the equivalent binary number.
It is worth noting that the binary system has few constraints in comparison to the decimal system.
For instance, the binary system is unable to portray fractions, so it is solely suitable for representing whole numbers.
The binary system further requires more digits to portray 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 long string of 0s and 1s can be prone to typos and reading errors.
Last Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has a lot of merits over the decimal system. For example, the binary system is much simpler than the decimal system, as it only 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 further fitted to depict information in digital systems, such as computers, as it can simply be portrayed utilizing electrical signals. As a consequence, knowledge of how to transform between the decimal and binary systems is essential for computer programmers and for unraveling mathematical problems including huge numbers.
Although the method of converting decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are applications that can rapidly convert between the two systems.
