The decimal and binary number systems are the world’s most commonly used number systems today.
The decimal system, also under the name of the base-10 system, is the system we utilize in our daily lives. It utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. At the same time, the binary system, also known as the base-2 system, uses only two digits (0 and 1) to represent numbers.
Understanding how to transform from and to the decimal and binary systems are essential for various reasons. For example, computers use the binary system to portray data, so computer programmers are supposed to be proficient in converting within the two systems.
Additionally, comprehending how to change between the two systems can help solve mathematical problems concerning large numbers.
This article will cover the formula for changing decimal to binary, give a conversion table, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of transforming 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) found in the previous step by 2, and record the quotient and the remainder.
Reiterate the prior steps before the quotient is equivalent to 0.
The binary equal of the decimal number is acquired by inverting the sequence of the remainders received in the previous steps.
This may sound complicated, 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 inverting 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 few instances of decimal to binary transformation utilizing the steps 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 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 equal of 128 is 10000000, which is obtained by inverting the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps defined prior offers a way to manually change decimal to binary, it can be tedious and error-prone for large numbers. Fortunately, other systems can be employed to rapidly and effortlessly change decimals to binary.
For example, you can employ the built-in features in a calculator or a spreadsheet program to convert decimals to binary. You can further use web-based applications for instance binary converters, that allow you to type a decimal number, and the converter will automatically produce the equivalent binary number.
It is important to note that the binary system has few constraints compared to the decimal system.
For instance, the binary system fails to portray fractions, so it is solely fit for representing whole numbers.
The binary system also requires more digits to illustrate a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, that has six digits. The long string of 0s and 1s can be inclined to typos and reading errors.
Concluding Thoughts on Decimal to Binary
In spite of these limitations, the binary system has some advantages over the decimal system. For instance, the binary system is much simpler than the decimal system, as it only uses two digits. This simpleness makes it simpler to carry out mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is further suited to representing information in digital systems, such as computers, as it can simply be portrayed using electrical signals. As a consequence, understanding how to change between the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems involving large numbers.
While the method of converting decimal to binary can be time-consuming and prone with error when worked on manually, there are applications which can quickly convert among the two systems.
