The decimal and binary number systems are the world’s most frequently utilized number systems presently.
The decimal system, also known as the base-10 system, is the system we use in our daily lives. It utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. However, the binary system, also known as the base-2 system, uses only two digits (0 and 1) to represent numbers.
Learning how to convert between the decimal and binary systems are important for many reasons. For instance, computers utilize the binary system to depict data, so computer engineers must be expert in converting among the two systems.
Additionally, learning how to change among the two systems can helpful to solve math problems concerning large numbers.
This article will cover the formula for transforming decimal to binary, offer a conversion table, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The procedure of changing a decimal number to a binary number is done manually utilizing the following steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) collect in the last step by 2, and note the quotient and the remainder.
Reiterate the previous steps unless the quotient is equivalent to 0.
The binary equal of the decimal number is acquired by reversing the sequence of the remainders obtained in the previous steps.
This might sound confusing, so here is an example to portray 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 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 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 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 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).
Even though the steps outlined prior provide a method to manually convert decimal to binary, it can be labor-intensive and error-prone for big numbers. Luckily, other ways can be utilized to swiftly and simply change decimals to binary.
For instance, you could employ the incorporated features in a spreadsheet or a calculator program to convert decimals to binary. You could additionally use web tools for instance binary converters, which allow you to enter a decimal number, and the converter will spontaneously generate the corresponding binary number.
It is important to note that the binary system has few constraints compared to the decimal system.
For instance, the binary system cannot represent fractions, so it is only suitable for representing 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 portrayed by the binary number 1100100, which has six digits. The extended string of 0s and 1s can be prone to typos and reading errors.
Last Thoughts on Decimal to Binary
In spite of these restrictions, the binary system has several advantages with the decimal system. For example, the binary system is lot easier than the decimal system, as it just uses two digits. This simplicity makes it easier to perform mathematical operations in the binary system, such as addition, subtraction, multiplication, and division.
The binary system is further fitted to depict information in digital systems, such as computers, as it can easily be represented utilizing electrical signals. Consequently, knowledge of how to change between the decimal and binary systems is essential for computer programmers and for unraveling mathematical problems including large numbers.
Even though the method of changing decimal to binary can be labor-intensive and vulnerable to errors when worked on manually, there are applications that can quickly convert within the two systems.
