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 utilize in our daily lives. It employees ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. On the other hand, the binary system, also known as the base-2 system, uses only two figures (0 and 1) to represent numbers.
Learning how to transform from and to the decimal and binary systems are essential for multiple reasons. For instance, computers use the binary system to represent data, so computer programmers should be proficient in changing between the two systems.
Additionally, comprehending how to convert among the two systems can help solve mathematical questions concerning enormous numbers.
This blog article will go through the formula for converting decimal to binary, give a conversion table, and give instances of decimal to binary conversion.
Formula for Converting Decimal to Binary
The procedure of transforming 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 note the quotient and the remainder.
Reiterate the last steps unless the quotient is similar to 0.
The binary corresponding of the decimal number is obtained by reversing the series of the remainders received in the last steps.
This might sound complex, 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 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 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 some examples of decimal to binary conversion utilizing the steps discussed earlier:
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 acquired by reversing the series 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 acquired by inverting the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined prior offers a way to manually convert decimal to binary, it can be time-consuming and open to error for big numbers. Fortunately, other ways can be used to rapidly and easily change decimals to binary.
For example, you could use the built-in functions in a spreadsheet or a calculator program to change decimals to binary. You could further use online applications for instance binary converters, which enables you to type a decimal number, and the converter will spontaneously generate the corresponding binary number.
It is worth noting that the binary system has few limitations in comparison to the decimal system.
For example, the binary system is unable to portray fractions, so it is solely fit for dealing with whole numbers.
The binary system further needs more digits to portray a number than the decimal system. For instance, the decimal number 100 can be portrayed by the binary number 1100100, that has six digits. The long string of 0s and 1s can be liable to typos and reading errors.
Concluding Thoughts on Decimal to Binary
Regardless these limitations, the binary system has some advantages with the decimal system. For example, the binary system is far simpler than the decimal system, as it only uses two digits. This simpleness makes it easier to conduct mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more suited to representing information in digital systems, such as computers, as it can simply be portrayed utilizing electrical signals. As a result, knowledge of how to change among the decimal and binary systems is essential for computer programmers and for unraveling mathematical questions involving large numbers.
Although the method of converting decimal to binary can be tedious and prone with error when done manually, there are tools that can rapidly convert between the two systems.
