Discussing basic concepts about Number Systems
Digital Circuits and Logic Designs #002
Table of contents
· Table of contents
∘ How is the number system used in real life?
· Decimal number system
· Binary number system
· Octal number system
· Hexadecimal number system
· Number Conversions
∘ Decimal to Binary conversion
∘ Binary to Decimal conversion
∘ Decimal to Octal conversion
∘ Octal to Decimal conversion
∘ Binary to Octal conversion
∘ Decimal to Hexadecimal conversion
∘ Hexadecimal to Decimal conversion
∘ Binary to Hexadecimal conversion
∘ Bonus method
The number system is a method to notify or represent the numbers of a given set or identity using symbols of relative significance. There are different types of number systems in which a single number can be represented in multiple ways.
How is the number system used in real life?
The number system helps us identify the extent to which we need to limit an entity. These give us a general insight into the mathematical operations regarding the given numbers. This helps in the calculation of numbers using mathematical operations. Visit more about how the number system is used in real life.
In the number system, numbers can be seen from different types of bases, and one needs to know how to convert them as needed. Although there are various technical methods for that, it is important to know how to do it alone with someone’s words in the basic foundation of learning information technology. I hope to talk about how to easily convert numbers between these different bases and some other important points.
I am using my handwritten notes here because it is easy to understand.
Decimal number system
Decimal is a numbering system that uses a base-10 representation for numeric values. The system is used extensively in everyday life to carry out routine tasks such as buying groceries, trading stocks, tracking football scores, or scrolling through cable channels. Numbers such as 7, 28, 199, and 532.11 are all examples of decimal numbers. The decimal system is also referred to as the Hindu-Arabic system. Additionally, the term decimal is often used to refer to a fraction that is represented as a number in the decimal system, such as 19.368. Learn more about decimals.
Binary number system
A binary number system is one of the four types of number systems. In computer applications, binary numbers are represented by only two symbols or digits, i.e., 0 (zero) and 1 (one). The binary numbers here are expressed in the base-2 numeral system. For example, (101)2 is a binary number. Each digit in this system is said to be a bit. Learn more about binary.
Octal number system
The Octal Number System has a base of eight and uses the numbers from 0 to 7. The octal numbers, in the number system, are usually represented by binary numbers when they are grouped in pairs of three. For example, an octal number 128 is expressed as 0010102 in the binary system, where 1 is equivalent to 001 and 2 is equivalent to 010. Learn more about octal.
Hexadecimal number system
The hexadecimal number system is a type of number system that has a base value equal to 16. It is also pronounced sometimes as ‘hex’. Hexadecimal numbers are represented by only 16 symbols. These symbols or values are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. Each digit represents a decimal value. Learn more about hexadecimal.
Number Conversions
As we know, the number system is a way of expressing numbers. In number system conversion, we will study how to convert one base, to a number of another base. There are a variety of number systems, such as binary numbers, decimal numbers, hexadecimal numbers, and octal numbers, that can be exercised.
Here, you will learn the conversion of one base number to another base number, considering all the base numbers such as decimal, binary, octal, and hexadecimal, with the help of examples. Here, the following number system conversion methods are explained:
Decimal to Binary conversion
In decimal-to-binary conversion, we convert a base 10 number to a base 2 number by using simple methods. For example, if 335(10) is a decimal number, then its equivalent binary number is 101001111(2). Thus, it is easy to convert the given decimal to binary using simple tricks, which you will learn here. Learn more.
Binary to Decimal conversion
Binary-to-decimal conversion explains the conversion of a binary number (base-2) to an equivalent decimal number (base-10). In mathematics, a number system is used for expressing numbers. It is a way to represent numbers. Learn more.
Decimal to Octal conversion
To convert a decimal to an octal, we have to learn about both number systems first. A number with base 8 is the octal number, and a number with base 10 is the decimal number. Here we will convert a decimal number to an equivalent octal number. Learn more.
Octal to Decimal conversion
In some cases, this method becomes difficult. Therefore, these methods are not widely used. An easy method is given below.
Binary to Octal conversion
These methods are not very popular. But it is a very easy method. Here, the corresponding binary value is divided into 3 parts from the end. Then 0 is added in front of the middle bit at the beginning. Then the values of those parts are obtained separately, as shown below.
Decimal to Hexadecimal conversion
You can learn things about using this.
Hexadecimal to Decimal conversion
As we know, number systems can be converted from one base to another. Thus, we can convert hexadecimal numbers to decimals easily. This number system conversion can be done as explained in the example given below: Learn more.
Binary to Hexadecimal conversion
Also, these methods are not very popular. But it is a very easy method. Here, the corresponding binary value is divided into 4 parts from the end. Then 0 is added in front of the middle bit at the beginning. Then the values of those parts are obtained separately, as shown below.
Bonus method
In some cases, it is quite difficult to convert decimal values to octal or hexadecimal values at the same time. In such cases, it is easier to first convert the decimal value to a binary value and then convert it to octal or hexadecimal values as needed.
Here we have simply talked about what a number system is, different number systems, and how to convert them to each other. I hope to talk more about this in the future.
Hope you get something new from it. Don’t forget to share it with the community, too, so they can also benefit from this context.
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