Conversion of a Number

The numeral system, commonly known as the number system, is the system that constitutes numbers. A number can be expressed as a mathematical value that helps in counting and measuring objects by performing several mathematical calculations. In a number system, there are different types of numbers including the binary numbers with base 2, octal numbers with base 8, decimal numbers with base 10, and hexadecimal numbers with base 16.  

Further, these numbers can be converted into different systems such as decimal to binary, decimal to octal, hexadecimal to decimal, and so on. In the decimal to binary conversion, the base 10 number is converted to the base 2 number through simple and unique methods, which we will be discussing today in this study material notes.  

This article talks about the conversion of a number in a decimal system to a binary system and vice-versa. You will find brief information on the concept of the number system in Maths, a thorough explanation of decimal to binary conversion, and other related topics. So, let’s start by describing the conversion of a number in a decimal system to a binary system in the Maths study material.

Explain number system in maths 

A number system can be described as a process of writing and expressing numbers. It is often referred to as a mathematical representation of numbers using a given set of digits or numbers in a consistent manner. It promotes easy arithmetic operations such as addition, subtraction, multiplication, and division. There are three ways to determine the value of any digit of a number. These are as follows – 

• The digit. 

• The base of the number system. 

• The position of the digit in the number. 

Decimal to binary conversion 

As mentioned in the introduction, the decimal number constitutes the base 10, whereas the binary number has the base 2. When the decimal to binary conversion takes place, the base of the number also interchanges, which means the base of the decimal number will be 2, whereas the base of the binary number will be 10. The decimals have the same binary numbers, mainly used in computer applications for programming and coding purposes. Every time the input is given to the computer system in the decimal form, it is further converted into binary digits, performs its functions and provides the required output. 

Steps of converting decimal numbers to binary numbers 

There are different methods and formulas through which the decimal numbers can be converted into binary numbers. Here are the following steps through which the decimal numbers can be converted into binary numbers. 

Step 1: The given decimal number should be divided by 2 to give the result leaving the remainder behind. 

Step 2: In case the decimal number is even, let’s say, 2, 4,6,8,  and so on, the remainder will be zero. 

Step 3: In case the decimal number is odd, let’s say, 3,5,7,9 and so on, the remainder will always be 1. 

Step 4: By placing the reminders in a single order so that the Least Significant Bit is placed at the top whereas, the Most Significant Bit is at the bottom. In such cases, the required binary number can be obtained. 

Converting the number 294 in the binary number –  

Decimal to binary table 

Here is the decimal to binary conversion table –  

Binary to decimal conversion steps 

Here are the binary to decimal conversion steps – 

• The first step involves writing the binary number and counting the two powers starting from right to left. 

• In the second step, write every binary digit from right to left with the power of 2 in a way that the first binary digit, which is MSB, is multiplied with the largest power of 2. 

• In the third step, add all the products one by one. 

• The answer will be the required decimal number. 

Conclusion 

With this, we come to an end to the conversion of a number in a decimal system to a binary system and vice versa. There are different types of numbers, including binary numbers, octal numbers, decimal numbers, and hexadecimal numbers.

In this article describing the conversion of a number in a decimal system to a binary system and vice-versa, we studied the concept of the number system in length. We covered several other topics, such as the conversion of decimal numbers to binary numbers and vice versa, and other related topics. We hope this study material helped you better understand the conversion of a number in the decimal system to binary system and vice-versa.