The decimal and binary number systems are the world’s most frequently utilized number systems right now.
The decimal system, also called the base-10 system, is the system we utilize in our daily 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 digits (0 and 1) to represent numbers.
Understanding how to transform from and to the decimal and binary systems are vital for multiple reasons. For example, computers use the binary system to represent data, so computer engineers should be expert in changing among the two systems.
In addition, comprehending how to convert between the two systems can be beneficial to solve math problems involving large numbers.
This blog article will go through the formula for changing decimal to binary, provide a conversion chart, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The procedure of transforming a decimal number to a binary number is performed manually using 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 record the quotient and the remainder.
Replicate the last steps until the quotient is equal to 0.
The binary equivalent of the decimal number is obtained by reversing the sequence of the remainders received in the prior steps.
This might sound complex, 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 equal 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 depicting 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 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, which is gained 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, that is obtained by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps described earlier provide a way to manually convert decimal to binary, it can be time-consuming and error-prone for large numbers. Thankfully, other systems can be utilized to swiftly and simply convert decimals to binary.
For instance, you could employ the incorporated functions in a spreadsheet or a calculator program to change decimals to binary. You can additionally utilize online tools for instance binary converters, that allow you to type a decimal number, and the converter will automatically generate the equivalent binary number.
It is important to note that the binary system has few limitations compared to the decimal system.
For example, the binary system fails to illustrate fractions, so it is only appropriate for representing whole numbers.
The binary system additionally needs more digits to represent a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The length string of 0s and 1s can be liable to typos and reading errors.
Concluding Thoughts on Decimal to Binary
Despite these limits, the binary system has several merits with 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 carry out mathematical functions in the binary system, for instance 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. Consequently, knowledge of how to convert among the decimal and binary systems is crucial for computer programmers and for solving mathematical problems including huge numbers.
While the method of changing decimal to binary can be tedious and error-prone when worked on manually, there are tools which can quickly change between the two systems.
