The decimal and binary number systems are the world’s most commonly utilized number systems presently.
The decimal system, also known as the base-10 system, is the system we utilize 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, utilizes only two figures (0 and 1) to depict numbers.
Comprehending how to transform from and to the decimal and binary systems are important for various reasons. For example, computers use the binary system to portray data, so computer programmers should be competent in converting among the two systems.
Furthermore, learning how to convert among the two systems can be beneficial to solve math problems concerning large numbers.
This article will go through the formula for transforming decimal to binary, provide a conversion chart, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of changing a decimal number to a binary number is done manually utilizing the ensuing 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.
Replicate the previous steps unless the quotient is equivalent to 0.
The binary corresponding of the decimal number is acquired by inverting the series of the remainders obtained in the previous steps.
This may sound confusing, 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 obtained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table showing 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 transformation employing the method discussed 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 equivalent of 25 is 11001, that 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 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 described prior provide a way to manually convert decimal to binary, it can be labor-intensive and open to error for big numbers. Fortunately, other methods can be used to rapidly and effortlessly convert decimals to binary.
For example, you can utilize the built-in functions in a spreadsheet or a calculator program to convert decimals to binary. You could further use web-based tools such as binary converters, that enables you to input a decimal number, and the converter will automatically generate the corresponding binary number.
It is worth pointing out that the binary system has handful of limitations compared to the decimal system.
For instance, the binary system cannot illustrate fractions, so it is solely suitable for representing whole numbers.
The binary system also 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 could be liable to typos and reading errors.
Last Thoughts on Decimal to Binary
Regardless 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 carry out mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is more fitted to representing information in digital systems, such as computers, as it can easily be depicted utilizing electrical signals. As a consequence, understanding how to change among the decimal and binary systems is essential for computer programmers and for unraveling mathematical questions concerning huge numbers.
Even though the process of converting decimal to binary can be tedious and prone with error when done manually, there are applications that can quickly change between the two systems.
