The decimal and binary number systems are the world’s most frequently used number systems right now.
The decimal system, also known as the base-10 system, is the system we use in our daily lives. It uses ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. On the other hand, the binary system, also called the base-2 system, utilizes only two figures (0 and 1) to depict numbers.
Learning how to transform from and to the decimal and binary systems are vital for multiple reasons. For instance, computers use the binary system to represent data, so software engineers must be proficient in converting within the two systems.
Additionally, learning how to change among the two systems can be beneficial to solve math problems concerning enormous numbers.
This blog article will go through the formula for transforming decimal to binary, offer a conversion table, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of converting a decimal number to a binary number is done manually using the following steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) found in the previous step by 2, and record the quotient and the remainder.
Replicate the previous steps until 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 previous steps.
This might sound complex, so here is an example to portray 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 gained 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 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 some examples of decimal to binary conversion employing the method talked about priorly:
Example 1: Convert 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 sequence of remainders (1, 1, 0, 0, 1).
Example 2: Convert 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 achieved by reversing 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 error-prone for large numbers. Fortunately, other systems can be utilized to rapidly and easily change decimals to binary.
For instance, you could use the built-in features in a spreadsheet or a calculator program to change decimals to binary. You can also use web-based tools similar to binary converters, which enables you to type a decimal number, and the converter will automatically produce the respective binary number.
It is worth noting that the binary system has handful of limitations compared to the decimal system.
For instance, the binary system fails to illustrate fractions, so it is solely suitable for dealing with 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, that has six digits. The long string of 0s and 1s could be inclined to typing errors and reading errors.
Final Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has several merits with the decimal system. For instance, the binary system is lot easier than the decimal system, as it only uses two digits. This simplicity makes it easier to carry out mathematical functions in the binary system, such as 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 depicted using electrical signals. As a consequence, knowledge of how to transform between the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems including huge numbers.
While the method of changing decimal to binary can be tedious and vulnerable to errors when done manually, there are applications which can rapidly convert within the two systems.
