Number System
The Number System is the set of guidelines that gives meaning to expressions written in that number system. For example, if we want to express that we have ten dogs, in the decimal number system we would write “10 dogs,” in the binary system “1010 dogs,” in the octal system “12 dogs,” and in the hexadecimal system “A dogs.” All these statements represent ten dogs but in different number systems.
Any Number System needs two things to express all the numbers we want it to represent. First are the symbols (generally all number systems that need less than or equal to 10 symbols use modern-day decimal numerals), and the second is the base (which is the number of required symbols). For example, in the decimal number system, there are ten symbols, so its base is 10.
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Decimal Number System
The Decimal Number System is the most used number system out of all. There are 10 digits in this number system, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The decimal numbers are represented as,
Binary Number System
In the Binary Number System, there are only two digits, and using those, we express all the numbers. The most common numerals for the Binary System are 0 and 1, but we can use any pair of symbols to represent the same as long as the symbols are well-defined. For example, 10010001, 11011001, and 1010 are some examples of binary numbers which in decimals represent 145, 217, and 10 respectively.
For a Better understanding of the conversion of binary to decimal read this article. In the binary system, we use two bits 0 and 1 as shown in the image below,
Octal Number System
In the Octal Number System, there are only 8 digits or symbols which are generally represented with modern-day decimal symbols by only up to 7 i.e., 0, 1, 2, 3, 4, 5, 6, 7. Using these 8 symbols we can write and express all the numbers. For example, 231, 41, and 653 are some examples of octal numbers which in decimals represent 153, 33, and 427 respectively. The digits used in the Octal Number system are shown in the image below,
Hexadecimal Number System
In the Hexadecimal Number System, there are 16 numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. It is widely used in programming-related tasks as its base is 16 (which is a multiple of 2), which is the foundation of computing as every bit can only have two values: on or off. Some examples of the Hexadecimal Number System are A1, 2A, and F3, which in the decimal number system represent 161, 42, and 243, respectively.
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What are Numbers?
Numbers in math are the most fundamental thing invented by mankind to serve its vast variety of endeavors in science and technology. From sending rockets to Mars to calculating bills for groceries, numbers are used everywhere. Nowadays, we can’t think of mathematics without Understanding numbers.
There are different types of numbers like natural numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers, prime numbers, composite numbers, algebraic numbers, transcendental numbers, even and odd numbers, and many, many more.
In this article, we will discuss what are numbers with examples, definition, types, history, operations on numbers, and practice problems.
Table of Content
- What are Numbers in Maths?
- Numbers Definition
- History of Numbers
- Classification of Numbers
- Operations on Numbers
- Division
- Multiplication
- Addition
- Subtraction
- Types of Numbers
- Prime Factorization
- HCF
- LCM
- Number System
- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System
- Properties of Numbers
- Solved Examples on What are Numbers