The decimal and binary number systems are the world’s most frequently utilized number systems right now.
The decimal system, also known as the base-10 system, is the system we utilize in our everyday lives. It utilizes ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. On the other hand, the binary system, also known as the base-2 system, uses only two figures (0 and 1) to represent numbers.
Comprehending how to convert between the decimal and binary systems are vital for multiple reasons. For instance, computers use the binary system to represent data, so computer engineers are supposed to be competent in converting within the two systems.
Additionally, learning how to change within the two systems can help solve math problems involving large numbers.
This blog will cover the formula for changing decimal to binary, provide 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 using the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) collect in the previous step by 2, and note the quotient and the remainder.
Repeat the last steps until the quotient is equal to 0.
The binary corresponding of the decimal number is obtained by inverting the sequence of the remainders acquired in the prior steps.
This might sound complicated, so here is an example to illustrate 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 chart portraying 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 examples of decimal to binary conversion using the steps discussed priorly:
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 equivalent of 25 is 11001, that is gained by reversing the sequence 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 sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined earlier provide a method to manually change decimal to binary, it can be tedious and open to error for large numbers. Thankfully, other ways can be utilized to swiftly and simply convert decimals to binary.
For example, you could utilize the incorporated functions in a spreadsheet or a calculator program to convert decimals to binary. You could further use web tools such as binary converters, that allow you to input a decimal number, and the converter will spontaneously produce the corresponding binary number.
It is worth noting that the binary system has some limitations in comparison to the decimal system.
For example, the binary system fails to represent 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 instance, the decimal number 100 can be portrayed by the binary number 1100100, that has six digits. The extended string of 0s and 1s could be prone to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Regardless these limits, the binary system has several advantages over the decimal system. For instance, the binary system is much simpler than the decimal system, as it only uses two digits. This simpleness makes it simpler to perform mathematical operations in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is more suited to representing information in digital systems, such as computers, as it can simply be depicted using electrical signals. Consequently, knowledge of how to transform between the decimal and binary systems is important for computer programmers and for solving mathematical problems concerning large numbers.
Although the process of changing decimal to binary can be tedious and error-prone when worked on manually, there are tools which can quickly change within the two systems.
