The decimal and binary number systems are the world’s most commonly used number systems right now.
The decimal system, also known as the base-10 system, is the system we utilize in our everyday lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. On the other hand, the binary system, also called the base-2 system, utilizes only two figures (0 and 1) to portray numbers.
Learning how to convert between the decimal and binary systems are essential for many reasons. For example, computers use the binary system to depict data, so software engineers must be competent in changing between the two systems.
In addition, learning how to change between the two systems can be beneficial to solve mathematical problems concerning large numbers.
This blog article will go through the formula for transforming decimal to binary, offer a conversion table, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The procedure of changing a decimal number to a binary number is done manually utilizing the ensuing steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) obtained in the last step by 2, and note the quotient and the remainder.
Repeat the last steps unless the quotient is equivalent to 0.
The binary equal of the decimal number is acquired by reversing the sequence of the remainders received in the prior steps.
This might sound complicated, so here is an example to illustrate 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 equivalent 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 table depicting 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 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 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 equivalent of 128 is 10000000, which is obtained by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps defined prior provide a method to manually change decimal to binary, it can be tedious and prone to error for big numbers. Fortunately, other ways can be used to quickly and easily change decimals to binary.
For example, you can employ the built-in features in a calculator or a spreadsheet program to change decimals to binary. You could further use online applications such as binary converters, that enables you to enter a decimal number, and the converter will spontaneously produce the corresponding binary number.
It is worth noting that the binary system has few limitations contrast to the decimal system.
For instance, the binary system is unable to represent fractions, so it is solely suitable for representing whole numbers.
The binary system further needs more digits to represent 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 long string of 0s and 1s could be prone to typing errors and reading errors.
Final Thoughts on Decimal to Binary
Despite these limitations, the binary system has several advantages with the decimal system. For example, the binary system is lot easier than the decimal system, as it only utilizes two digits. This simpleness makes it easier to carry out mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is more suited to depict information in digital systems, such as computers, as it can easily be represented using electrical signals. Consequently, understanding how to change among the decimal and binary systems is important for computer programmers and for solving mathematical questions including huge numbers.
While the method of changing decimal to binary can be tedious and vulnerable to errors when worked on manually, there are applications which can quickly change within the two systems.
