Number system

Number Systems — Decimal, Binary, Octal, and Hexadecimal
Base 10 (Decimal) — Represent any number using 10 digits [0–9]
Base 2 (Binary) — Represent any number using 2 digits [0–1]
Base 8 (Octal) — Represent any number using 8 digits [0–7]
Base 16(Hexadecimal) — Represent any number using 10 digits and 6 characters [0–9, A, B, C, D, E, F]

1. NUMBER SYSTEM

2. Presented By  1. Anirban saha   anik             18-36207-1 2 . bishowjit   Datta               18-37372-1 3 .  Zubaer Hossain Asif        18-36248-1 4 .   Lutfa noor labony           18-36187-1 Submitted to :  SYED MD. ANWARUL ISLAM

3. What Is number system ? A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction and division. The value of any digit in a number can be determined by: The digit Its position in the number The base of the number system Types of Number System: There are various types of number system in mathematics. The four most common number system types are: Decimal number system (Base- 10) Binary number system (Base- 2) Octal number system (Base-8) Hexadecimal number system (Base- 16)

4. Decimal Number Systems

5. In algebra, a decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one. Example : The numbers we use in everyday life are  decimal numbers , because they are based on 10 digits (0,1,2,3,4,5,6,7,8 and 9) DECIMAL NUMBER

6. Applications Of Decimal In Daily Life:  We use decimals every day while dealing with money, weight, length etc. Decimal numbers are used in situations where more precision is required than the whole numbers can provide. For example, when we calculate our weight on the weighing machine, we do not always find the weight equal to a whole number on the scale. To know our exact weight, we must understand what the decimal value on the scale means. This section deals with the concept of decimals in three important fields of our daily life.

7. Use of decimal to Represent the weight: We use decimal numbers while dealing with weight. For example, when we are buying a watermelon, it cannot always weigh in whole numbers, it can be less than 2 kg but more than 1 kg. In such situations, the shopkeeper has to calculate how much to charge for a watermelon, based on its weight. As we know,  1 kg = 1000 gm 1 gm = 1000 mg Now suppose it is 1 kg and 750 gm. Then, he will charge as per the price of 1 kg + (750/1000) kg of the watermelon. We will learn more about the conversion of weight into decimal from the following examples:  Example 1: Converting 250 gm to kg As we know, 1000 gm = 1 kg  So, 1 gm = 1/1000 kg  250 gm = 250 × (1/1000) kg = 250/1000 kg = 0.250 kg

8. Binary Number  System

9. Binary Number In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically "0" (zero) and "1" (one ). Each digit is referred to as a bit. Example:  0 1 1 is a binary number and the decimal value is 6.

10. Bits and binary Computers use  binary  - the digits 0 and 1 - to store data. A binary digit, or  bit , is the smallest unit of data in computing. The circuits in a computer's processor are made up of billions of  transistors . A transistor is a tiny switch that is activated by the electronic signals it receives.  The digits 1 and 0 used in binary reflect the on and off states of a transistor . Computer programs are sets of instructions. Each instruction is translated into  machine code  - simple binary codes that activate the  CPU .

11. Binary coded decimal (BCD) Binary codded decimal is simply another way in which denary numbers can be written as  binary.It  simply details splitting up a binary number into equal portions of bits. So an 8 bit binary  number  may be split in half as shown below. 00111000 0011   1000   3           8 Binary coded decimal would be 3 8 this method is widely used in clocks as with the one shown :

12. BINARY & THE INTERNET PROTOCOL As explained during the introduction, computers display the zeros and ones in a way that makes the information useful to us. The Internet Protocol works a bit like this as well, where 98% of the time we see it in a decimal notation, but the computer understands it in binary. The picture below gives you an example of how a computer understands an IP Address: The above example shows an IP address in decimal notation, which we understand more easily, this IP Address - 192.168.0.1 is then converted to Binary, which is what the computer understands and you can see how big the number gets ! It's easier for us to remember 4 different numbers than 32 zeros or ones !

13. Octal Number system  

14. Octal Number The number system whose base is 8 is known as the octal number system. The base 8 means the system uses eight digits from 0 to 7. Example  : Consider the octal number 354.42 into its equivalent decimal number. The integer part 354 converts to octal shown below                                        3(8 2 )+5(8 1 )+4(8 )=236

15. Octal used to be used widely within IT basically how hexadecimal is used today. It was used as an ideal abbreviation of binary because the bit size (amount of bits that could be handled at one go) of the CPUs that were used at the time that being 26 and 36 bit. After CPUs converted to bit sizes of 32 and 64 bit octal was no longer utilized because, though both are still dividable by 8 they can also be divided by 16 which is far more efficient. There are some places however where octal is still widely utilized including within file permissions within unix (the source code for linux , mac os and android along with other operating systems) to avoid having to add support for symbols for hexadecimal. It is also used within digital displays that also have no support for symbols. Use of The Octal Number System in Computer System

16. All modern computers use binary for their internal storage. This is due to the ease the hardware can represent binary values (on or off). However humans have issues dealing with large strings of binary numbers. For example, the number 128 decimal is 10000000 in binary. Larger numbers get even harder to deal with (for humans). However if binary numbers are grouped in groups of 3, then it is easy to view the numbers in octal. Or groups of 4 make hexadecimal numbers. So 128 decimal is 200 octal or 80 hex. It’s all the same number but the larger bases make it easier for humans to use . Octal Used for Easier Human Understanding

17. Octal Used in Minicomputers In early days octal number system was mostly used in minicomputers. The word “OCT” means eight. The octal number system says that it is a number system of base 8 which means that we require 8 different symbols in order to represent any number in octal system. The symbols are 0, 1, 2, 3, 4, 5, 6, and 7. The smallest two digits number in this system is (10) 8 which is equivalent to decimal 8. For example in this number system, the number is written as (352) 8 . The base should be written as 8 otherwise the number is assumed to be in decimal number system by default. So this thing needs to be taken care of in writing the number. A little error may result in the change in number system base. The main advantage of using octal number system is that it can be converted directly to binary in a very easy manner. As we know, the computer understands only the binary number system. so the conversion from binary to octal or from octal to binary is quite easier so this number system is used.

18. hexadecimal Number system

19. Hexadecimal Number In   mathematics and   computing,  hexadecimal (also base 16, or hex) is a  positional system  that represents numbers using a  base  of 16. Unlike the common way  of representing numbers with ten symbols, it uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values zero to nine, and "A"–"F" (or alternatively "a"–"f") to represent values ten to fifteen. The hexadecimal numeral system, often shortened to " hex. Example : The Decimal number of  16,295  can be represented as:- #3FA7 16   ( in Hexadecimal )

20.         Use of hexadecimal in IT applications Hexadecimal is also used within digital applications for a range of separate applications. One use of the hexadecimal number system within computer architecture is within RAM (Randomly access memory) within which each memory location (section of memory) being addressed (represented) with a hexadecimal number. Each hexadecimal digit represents a "nibble," which is half of a byte (4 bits), this means that bytes can also be represented in hexadecimal going from 0 (00) to 255 (FF) instead of just being represented in binary which can be harder to understand.  Another location within digital applications where the hexadecimal number system is used is within the web safe color pallet shown:

21.                  HTML / CSS Color Codes Hexadecimal numbers are often used to represent color within HTML  or CSS . The 6 digits hex color code should be considered in three parts. First two digits represents the amount of red in the color (max FF, or 255) The next two digits represent the amount of green in the color (max FF, or 255) The final two digits represent the amount of blue in the color (max FF, or 255) By changing the intensities of red, green and blue, we can create almost any color. Example : orange can be represented as #FFA500, which is (255 red, 165 green, 0 blue).

22.                      CONCLUSION  The number system is simply a system to represent or express numbers. There are various types of number systems and the most commonly used ones are decimal number system, binary number system, octal number system, and hexadecimal number system. Number system helps to represent numbers in a small symbol set. Computers, in general, use binary numbers 0 and 1 to keep the calculations simple and to keep the amount of necessary circuitry less, which results in the least amount of space, energy consumption and cost.