The decimal and binary number systems are the world’s most frequently used number systems today.
The decimal system, also known as the base-10 system, is the system we utilize 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, utilizes only two figures (0 and 1) to represent numbers.
Understanding how to transform from and to the decimal and binary systems are important for multiple reasons. For instance, computers utilize the binary system to depict data, so software programmers should be expert in changing between the two systems.
In addition, learning how to convert between the two systems can helpful to solve math problems involving enormous numbers.
This blog article will cover the formula for changing decimal to binary, offer a conversion chart, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The method of converting a decimal number to a binary number is done 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 document the quotient and the remainder.
Repeat the prior steps until the quotient is equal to 0.
The binary corresponding of the decimal number is achieved by inverting the sequence of the remainders obtained in the previous 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 equal of 75 is 1001011, which is obtained by inverting the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart portraying 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 few examples of decimal to binary transformation utilizing 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 equal of 25 is 11001, that 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 equivalent of 128 is 10000000, which is obtained by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described above offers a way to manually convert decimal to binary, it can be labor-intensive and error-prone for large numbers. Luckily, other systems can be used to rapidly and easily change decimals to binary.
For example, you could utilize the incorporated features in a calculator or a spreadsheet program to convert decimals to binary. You can additionally use web-based applications such as binary converters, which enables you to input a decimal number, and the converter will spontaneously produce the equivalent binary number.
It is important to note that the binary system has some constraints in comparison to the decimal system.
For instance, the binary system is unable to represent fractions, so it is only suitable for dealing with whole numbers.
The binary system also requires more digits to portray a number than the decimal system. For instance, 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 inclined to typing errors and reading errors.
Last Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has a lot of merits with the decimal system. For example, the binary system is much simpler than the decimal system, as it only utilizes two digits. This simplicity makes it simpler to perform mathematical operations in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further suited to representing information in digital systems, such as computers, as it can simply be represented using electrical signals. As a consequence, understanding how to convert among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems including large numbers.
While the process of converting decimal to binary can be tedious and error-prone when worked on manually, there are tools that can quickly convert among the two systems.
