The decimal and binary number systems are the world’s most frequently utilized number systems presently.
The decimal system, also called the base-10 system, is the system we use in our daily lives. It employees 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, uses only two digits (0 and 1) to represent numbers.
Comprehending how to transform from and to the decimal and binary systems are important for various reasons. For instance, computers utilize the binary system to portray data, so computer programmers are supposed to be proficient in converting within the two systems.
Furthermore, understanding how to change within the two systems can help solve math questions including large numbers.
This blog will cover the formula for converting decimal to binary, give a conversion chart, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The method of changing a decimal number to a binary number is done manually utilizing the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) collect in the last step by 2, and record the quotient and the remainder.
Replicate the previous steps unless the quotient is equal to 0.
The binary corresponding of the decimal number is acquired by reversing the series of the remainders obtained in the prior steps.
This might sound complicated, 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 obtained 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 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 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 acquired by inverting 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, that is acquired by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps defined earlier provide a way to manually change decimal to binary, it can be tedious and open to error for large numbers. Luckily, other systems can be employed to rapidly and effortlessly change decimals to binary.
For instance, you could utilize the built-in functions in a calculator or a spreadsheet application to convert decimals to binary. You can additionally use web applications such as binary converters, which enables you to enter a decimal number, and the converter will automatically generate the corresponding binary number.
It is important to note that the binary system has few limitations in comparison to the decimal system.
For instance, the binary system cannot portray fractions, so it is solely fit for dealing with whole numbers.
The binary system additionally requires more digits to represent a number than the decimal system. For example, the decimal number 100 can be represented by the binary number 1100100, that has six digits. The long string of 0s and 1s could be inclined to typos and reading errors.
Concluding Thoughts on Decimal to Binary
Despite these restrictions, the binary system has some merits with the decimal system. For example, the binary system is far simpler than the decimal system, as it just uses two digits. This simpleness makes it easier to conduct mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is further fitted to representing information in digital systems, such as computers, as it can effortlessly be depicted utilizing electrical signals. Consequently, understanding how to convert among the decimal and binary systems is important for computer programmers and for unraveling mathematical questions involving huge numbers.
Although the method of converting decimal to binary can be tedious and prone with error when worked on manually, there are applications which can easily convert among the two systems.
