The decimal and binary number systems are the world’s most frequently utilized number systems right now.
The decimal system, also known as the base-10 system, is the system we utilize in our everyday 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 depict numbers.
Learning how to convert between the decimal and binary systems are vital for various reasons. For instance, computers utilize the binary system to depict data, so computer engineers should be proficient in converting among the two systems.
Furthermore, learning how to convert between the two systems can helpful to solve math problems including large 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 following steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) obtained in the last step by 2, and document the quotient and the remainder.
Reiterate the prior steps until the quotient is equivalent to 0.
The binary equivalent of the decimal number is achieved by inverting the series of the remainders obtained in the previous steps.
This may sound complex, so here is an example to portray 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 acquired 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 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 instances 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 equal of 25 is 11001, which is obtained 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 obtained by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps outlined above offers a way to manually convert decimal to binary, it can be time-consuming and open to error for large numbers. Thankfully, other ways can be utilized to quickly and easily convert decimals to binary.
For example, you could utilize the incorporated features in a calculator or a spreadsheet application to change decimals to binary. You can also utilize web applications such as 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 compared to the decimal system.
For example, the binary system is unable to portray fractions, so it is only fit for dealing with whole numbers.
The binary system further needs more digits to illustrate 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 length string of 0s and 1s can be inclined to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Regardless these limits, the binary system has a lot of merits with the decimal system. For example, the binary system is far simpler than the decimal system, as it just utilizes two digits. This simpleness makes it simpler to conduct 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 effortlessly be depicted utilizing electrical signals. As a consequence, knowledge of how to change among the decimal and binary systems is important for computer programmers and for solving mathematical problems concerning huge numbers.
Although the method of changing decimal to binary can be tedious and prone with error when worked on manually, there are applications that can easily change within the two systems.
