# Number System

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A number system is a way of representing numbers using symbols. There are many different number systems, but the most common ones are decimal, binary, and hexadecimal. In the decimal system, which is also called the base-10 system, each digit from 0 to 9 represents a number. In the binary system, which is also called the base-2 system, each digit from 0 to 1 represents a number. In the hexadecimal system, which is also called the base-16 system, each digit from 0 to 9 and A to F represents a number. The number 5 can be represented as 101 in binary, or 5 in decimal. The number 12 can be represented as 1100 in binary, or C in hexadecimal. Here knowledge glow provides everything about number system.

## What Is a Number?

In mathematics, a number is a value that represents a quantity, such as 3 or 42. We use numbers in many ways, including to count objects, measure quantities, and label values. The number system we use the most often in daily life is the decimal system, which uses 10 digits (0–9). But there are other number systems too, such as binary (base 2) and hexadecimal (base 16).

## What Is Number System in Maths?

A number system is a way of representing numbers using symbols. The most common number system is the decimal system, which uses 10 symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent numbers.

Other number systems include the binary system (which uses two symbols: 0 and 1), and the hexadecimal system (which uses 16 symbols: 0-9 and A-F).

Number systems are important in mathematics as they provide a way to represent numbers in a concise and unambiguous manner. They also allow for easy manipulation of numbers and calculation of results.

## The Different Types of Number System

There are three different types of number systems: the decimal system, the binary system, octal number system and the hexadecimal system.

The decimal system is the most common type of number system. It uses a base-10 numbering system, which means that there are 10 possible digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The decimal system is used in everyday life to count things like money and measuring units (such as inches or centimeters).

The binary system is a base-2 numbering system. This means that there are only two possible digits: 0 and 1. The binary system is used in computer programming because it is very easy for computers to understand.

The hexadecimal system is a base-16 numbering system. This means that there are 16 possible digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 ,9 , A , B , C , D , E , F . The hexadecimal system is often used in computer programming because it is easier for humans to read than binary code.

Octal number system is a base-8 number system. The digits 0,1,2,3,4 and 5 are not used in the octal system. In this system all numbers are represented by the digits 0 through 7.

Also Read : What Are the Different Types of Numbers

## What Are the Advantages of Binary Over Decimal Number System?

Binary is a base 2 number system. This means that it uses only two digits, 0 and 1, for each number. In decimal numbers, you can add or subtract by using the digits of your own choice. You can also shift left or right by one place as well as multiply and divide numbers in binary systems by using only their base-2 equivalents. For example, if you have 100 in decimal (base 10), then 100 in binary would be 101010 because 1*2=2; 10 -1 = 9 (see below). If you have 0 in decimal (base 10), then 0 in binary would be 111011 since I=11….

## Why Do Computers Use the Binary Number System?

The binary number system is a more efficient way to store information than decimal. It uses only two symbols, 0 and 1, which reduces the total number of possible digits from 10 to 7. This means that each character requires just 2 bits (16 possible values) instead of 6 bits (2100). In addition, converting between base 10 and base 2 (decimal) takes less time with higher precision numbers than lower precision ones because there are fewer digits being processed at once; this also makes it easier for computers to process numbers in both ways without having to change their internal operation order or memory locations. Additionally, computers can access any part of their address space via logical rather than physical addresses which makes them faster when reading/writing data due either because this method doesn’t require additional steps during processing or because logical addressing allows accessing different parts simultaneously without waiting for all pieces before moving onto another item later on down stream.

## What Is Decimal Number System

The decimal number system is the most common and widely used number system in the world. It is also known as base 10, because it uses the ten digits 0 through 9 to represent any number. The decimal system has been used in western civilizations since ancient Greece, although various other numbering systems were employed at different times and places.

## How Do We Convert a Decimal Number to Binary Number?

Suppose you want to convert the decimal number 1234567890 into binary. To do so, firstly we need to decide on how many digits there will be in each group of our binary number. In other words, how many groups should we break up our integer?

For example: if we are going to use four groups then we can break up our integer 1234567890 into 4 parts of 8 bits each which would make a 32-bit value or 3 bytes (8 bit) worth of memory space used by this particular program. This may seem like overkill but it is necessary if you plan on storing large amounts of data in memory and need room for future expansion! However if your system has less than 32-bits available then there is no point in trying anything beyond this size because all systems have limitations when processing large amounts

Now that you know what type(s)

## How to Convert a Binary Number to Its Decimal Equivalent?

To convert a binary number to its decimal equivalent, you add zeros at the end of the binary number.

For example, if you wanted to know how many years it takes for 1 million seconds (1 million seconds = 60000 milliseconds) then you would have to add six zeroes after 1101 in order to get your answer: one billion seconds = 1000000000000 milliseconds.

## What Is Octal Number System?

Octal number system is a base-8 number system. The digits 0,1,2,3,4 and 5 are not used in the octal system. In this system all numbers are represented by the digits 0 through 7. The octal numbers that have been assigned to the powers of 2 are 8, 9, 10 and 11 respectively.

Octal numbers are used in computing to represent binary numbers as well as computer communication codes like ASCII or EBCDIC (Extended Binary Coded Decimal Interchange Code). Octal notation is also used in some programming languages such as COBOL (Common Business-Oriented Language) and FORTRAN for representing decimal expansion of integers with up to 4 decimal places

## How to Convert a Binary Number to Its Octal Equivalent?

To convert a binary number to its octal equivalent, you need to know the following:

• The first and last digits are the same. For example, if you have 1101 (11) as your binary number, then 1111 (1) is also an octal equivalent for that same value.
• The middle two digits are the same. For example, if you have 10011 as your binary value and want to convert it into its octal representation (or vice versa), then 1101 is also an octal representation of this same value!

## How to Convert an Octal Number to Its Binary Equivalent?

To convert an octal number to its binary equivalent, we need to divide the number by 8.

For example:

1/2 = 0, so 1/8 = 0 + 4 = 4

3/4 = 2, so 3/8 = 2 + 4 = 6

• To convert a decimal number into its hexadecimal equivalent: take the digits from both sides and add them up together.* For example, 5 means 00011010; which can be broken down into two groups: 5 + A (which is 10) and 2D (which is 01). So this would be written as “5AA” or “10A0”.

## What Is Hexadecimal Number System?

Hexadecimal number system is based on 16 symbols. It is used for representing numbers in computers and it’s also known as base 16, because each symbol represents a value from 0 to F (hexadecimal digits are from 0 to 9). The hexadecimal system represents binary numbers by using the digits A through F.

The following chart shows how you can convert a decimal number into its equivalent in hexadecimal format:

## What Is the Difference Between the Decimal, Binary, Octal and Hexadecimal Number Systems?

There are many ways to write a number in a computer. Each system uses different conventions and ways of representing numbers, but the basic idea is that each digit represents a power of 2 (2^1 = 1) or 3 (2^3 = 9).

The decimal number system uses 10 digits: 0 through 9, with symbols for the ones place (0), tens place (10), hundreds place (100), thousands place (1000), etc., ranging from left to right across the keyboard. This means that you can represent any number between 0 and 9 by simply adding up these ten numbers together:

0 + 1 + 2 + 3 + 4 + … += 10 => 100 – 10 => 90

This method works well for simple calculations like addition or subtraction since we don’t have to keep track of negative numbers as well! But if our goal was writing out long strings of digits then this wouldn’t work so well — especially since some computers only support 8-bit quantities!

## The Benefits of Using a Number System

Number systems are a way of representing numbers using symbols. The most common number system is the decimal system, which uses the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Other number systems include the binary system (which uses the symbols 0 and 1), the octal system (which uses the symbols 0, 1, 2, 3, 4, 5, 6, and 7), and the hexadecimal system (which uses the symbols 0–9 and A–F).

Number systems have a base, which is the number of different symbols used. For example, the decimal system has a base of 10 because it uses 10 different symbols: 0–9. The binary system has a base of 2 because it uses 2 different symbols: 0 and 1. The octal system has a base of 8 because it uses 8 different symbols: 0–7. The hexadecimal system has a base of 16 because it uses 16 different symbols: 0–9 and A–F.

The benefits of using a number system include being able to represent any number using a finite set of symbols and being able to perform operations on numbers using only those symbols.

## Conclusion

We hope this article helped you understand the various number systems used in mathematics and computer science. Each system has its own advantages and disadvantages, so it’s important to choose the right one for the task at hand. With a little practice, you should be able to easily convert between different number systems.

## Frequently Asked Questions on Number System

### What is a Number System?

A number system is a set of symbols that represent numbers and operations on them. The most commonly used number system today is the decimal system, which has ten symbols for digits: 0-9. In other systems, however, numbers are represented by different sets of symbols.

### What is the base of number syestm

The base of a number system is the number of different symbols that are used to represent numbers. In the decimal system, for example, the base is 10 because there are ten different digits (0-9).

### Why is the Number System Important?

The number system is important because it allows us to represent and perform calculations on numbers. Without a number system, we could not do math and would be unable to calculate measurements of length, weight, volume, area or temperature. In addition to basic arithmetic operations such as addition and subtraction, the number system also makes it possible for us to perform more advanced mathematical functions like multiplication and division.

### What is Base 1 Number System Called?

The base 1 number system is called unary numeral system and is the simplest numeral system to represent natural numbers.

### What is the equivalent binary number for the decimal number 435?

(435)10 in binary is equal to:
43510 = 1101100112