The decimal and binary number systems are the world’s most frequently utilized number systems today.
The decimal system, also called the base-10 system, is the system we use in our daily lives. It utilizes ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. However, the binary system, also called the base-2 system, employees only two figures (0 and 1) to portray numbers.
Learning how to convert between the decimal and binary systems are vital for multiple reasons. For example, computers utilize the binary system to portray data, so computer programmers must be proficient in converting between the two systems.
Furthermore, understanding how to convert between the two systems can help solve math problems concerning large numbers.
This blog will cover the formula for converting decimal to binary, provide 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 performed manually using the ensuing steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) obtained 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 corresponding of the decimal number is achieved by inverting the sequence of the remainders received in the last steps.
This may sound confusing, so here is an example to show you 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 reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart depicting 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 steps discussed earlier:
Example 1: Change 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 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 described prior provide a way to manually convert decimal to binary, it can be labor-intensive and prone to error for large numbers. Thankfully, other systems can be utilized to swiftly and easily convert decimals to binary.
For instance, you can utilize the incorporated functions in a calculator or a spreadsheet program to change decimals to binary. You can further use web-based applications for instance binary converters, which enables you to type a decimal number, and the converter will spontaneously generate the respective binary number.
It is important to note that the binary system has some constraints contrast to the decimal system.
For example, the binary system cannot portray fractions, so it is solely appropriate for representing whole numbers.
The binary system also needs more digits to portray a number than the decimal system. For instance, the decimal number 100 can be represented by the binary number 1100100, which has six digits. The long string of 0s and 1s can be liable to typos and reading errors.
Final Thoughts on Decimal to Binary
Despite these limits, the binary system has a lot of advantages over the decimal system. For example, the binary system is far simpler than the decimal system, as it just uses two digits. This simplicity makes it simpler to conduct mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is further fitted to representing information in digital systems, such as computers, as it can effortlessly be represented using electrical signals. As a consequence, understanding how to transform between the decimal and binary systems is essential for computer programmers and for solving mathematical problems concerning large numbers.
Even though the process of converting decimal to binary can be tedious and prone with error when worked on manually, there are applications which can easily change between the two systems.
