The decimal and binary number systems are the world’s most frequently used number systems right now.
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 illustrate numbers. However, the binary system, also known as the base-2 system, uses only two figures (0 and 1) to portray numbers.
Learning how to transform from and to the decimal and binary systems are important for multiple reasons. For instance, computers use the binary system to represent data, so software programmers should be competent in converting among the two systems.
Additionally, comprehending how to change among the two systems can help solve mathematical questions including enormous numbers.
This blog will go through the formula for changing decimal to binary, provide a conversion chart, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The procedure of converting a decimal number to a binary number is performed manually using the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) obtained in the last step by 2, and record the quotient and the remainder.
Repeat the last steps before the quotient is equivalent to 0.
The binary equivalent of the decimal number is achieved by reversing the sequence of the remainders received in the prior 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 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 some instances of decimal to binary transformation employing the method 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, which is obtained by reversing 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, which is achieved by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined prior offers a method to manually convert decimal to binary, it can be time-consuming and prone to error for big numbers. Thankfully, other systems can be utilized to swiftly and effortlessly change decimals to binary.
For example, you can utilize the built-in functions in a spreadsheet or a calculator application to change decimals to binary. You could also use web tools for instance binary converters, which allow 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 limitations compared to the decimal system.
For instance, the binary system is unable to portray fractions, so it is only appropriate 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, that has six digits. The length string of 0s and 1s could be liable to typos and reading errors.
Last Thoughts on Decimal to Binary
Despite these limitations, the binary system has some merits with the decimal system. For example, the binary system is far simpler than the decimal system, as it just utilizes two digits. This simpleness makes it simpler to conduct mathematical operations in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is more fitted to depict information in digital systems, such as computers, as it can simply be portrayed using electrical signals. As a result, understanding how to change between the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems involving huge numbers.
Even though the process of changing decimal to binary can be time-consuming and prone with error when done manually, there are applications which can quickly change between the two systems.
