The decimal and binary number systems are the world’s most frequently utilized 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 utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. However, the binary system, also known as the base-2 system, utilizes only two figures (0 and 1) to represent numbers.
Comprehending how to transform from and to the decimal and binary systems are important for many reasons. For example, computers utilize the binary system to portray data, so computer engineers are supposed to be expert in changing within the two systems.
In addition, learning how to change within the two systems can help solve mathematical problems concerning enormous numbers.
This article will cover the formula for converting decimal to binary, offer a conversion table, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The procedure of converting a decimal number to a binary number is done manually using the ensuing steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) obtained in the prior step by 2, and note the quotient and the remainder.
Replicate the last steps unless the quotient is equal to 0.
The binary corresponding of the decimal number is obtained by reversing the series of the remainders acquired in the prior steps.
This might sound confusing, so here is an example to illustrate this process:
Let’s convert 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 acquired by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table 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 transformation employing the method 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 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 acquired by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined earlier offers a way to manually change decimal to binary, it can be labor-intensive and error-prone for large numbers. Thankfully, other ways can be employed to swiftly and easily convert decimals to binary.
For instance, you could use the incorporated functions in a spreadsheet or a calculator application to convert decimals to binary. You can also use web-based applications similar to binary converters, that enables you to input a decimal number, and the converter will automatically generate the corresponding binary number.
It is important to note that the binary system has some constraints compared to the decimal system.
For example, the binary system fails to portray fractions, so it is only fit for dealing with whole numbers.
The binary system also requires more digits to portray a number than the decimal system. For example, the decimal number 100 can be represented 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 some advantages over the decimal system. For instance, the binary system is lot easier than the decimal system, as it just uses two digits. This simpleness makes it simpler to perform mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further fitted to depict information in digital systems, such as computers, as it can easily be portrayed utilizing electrical signals. Consequently, knowledge of how to convert among the decimal and binary systems is crucial for computer programmers and for solving mathematical problems concerning large numbers.
While the method of converting decimal to binary can be time-consuming and prone with error when done manually, there are tools which can easily change within the two systems.
