2.  Method of representing or encoding numbers  Two main notation types  Sign-value  Roman numerals  Positional (place-value)  Modern decimal notation  Several number systems are commonly used in computing  Decimal  Binary  Hexadecimal  “Shorthand” for binary Digital Data2

3.  We count in “decimal” or base 10 by powers of 10:  10 0 = 1  10 1 = 10  10 2 = 10*10 = 100  10 3 = 10*10*10 = 1,000  10 6 = 1,000,000  Computers count in “binary” or base 2:  2 0 = 1  2 1 = 2  2 2 = 2*2 = 4  2 3 = 2*2*2 = 8  2 10 = 1,024 Digital Data3

4.  Bit (b): bi nary digi t -- 0 or 1 value  0 or 1 correspond to the electrical values of off or on, respectively  All computer data is represented in bits  Byte (B): grouping of 8 bits  Considered the basic unit of digital information  8 bits = 1 byte is the de facto standard (also called an octet )  File sizes and network data are measured in bytes  You can’t have a 5-bit file  Physical network media transmit bits, but network protocols are based on bytes  Unit multiples  Kilobyte: 2 10 = 1,024 bytes (≈ 1,000)  Megabyte: 2 20 = 1,048,576 bytes (≈ 1,000,000)  Gigabyte: 2 30 = 1,073,741,824 bytes (≈ 1,000,000,000)  Terabyte: 2 40 = 1,099,511,627,776 bytes (≈ 1,000,000,000,000) Digital Data4

5.  Decimal  Binary  Hexadecimal Digit Position ( k ) 3210 Weight (b k ) 10 3 10 2 10 1 10 0 Decimal Weight1,000100101 Digit (a k ) 1983 Decimal Value 1,000900803 = 1,983 Digit Position ( k ) 109876543210 Weight (b k ) 2 10 2929 2828 2727 2626 2525 2424 23232 2121 2020 Decimal Weight1,0245122561286432168421 Digit (a k ) 11110 111111 Decimal Value 1,024512256128 0 3216 84 2 1 = 1,983 Digit Position ( k ) 210 Weight (b k ) 16 2 16 1 16 0 Decimal Weight256161 Digit (a k ) 7BF Decimal Value 1,79217615= 1,983 Digital Data5

6.  Base  Number around which system is organized  Number of symbols used to represent each digit of a number  Digits  Set of symbols used in forming numbers  Additional symbols may be defined for bases > 10  Ex: hexadecimal (see chart at right)  Positional Notation  Position of a digit conveys its significance  Rightmost digit represents the zero- power of the base value  Moving left, each digit represents an increasing power of the base number Number SystemBaseDigits Decimal 100,1,…, 9 Binary 20, 1 Hexadecimal 160, 1,…, 9, A – F Digit Position Number System 43210 Decimal 10 4 10,000 10 3 1,000 10 2 100 10 1 10 10 0 1 Binary 2 4 16 2382382 224224 212212 201201 Hexadecimal 16 4 65,536 16 3 4,096 16 2 256 16 1 16 16 0 1 Digital Data6

7.  Hexadecimal: A shorthand notation for binary  One hex digit represents 4 binary digits  Hexadecimal numbers are usually prefixed with “0x” to identify number it is a hex value  7BF 16 → 0x7BF Digital Data7 DecimalBinaryHex 000000 100011 200102 300113 401004 501015 601106 701117 DecimalBinaryHex 810008 910019 101010A 111011B 121100C 131101D 141110E 151111F

8. 1. Divide the value by the given base x  The remainder will be the least significant (right- most) digit of the base x number 2. Divide the result by the base  The remainder becomes the most significant (left- most) digit of the base x number 3. Repeat step 2 until the result is zero  The remainder is the most significant digit of the base x number Digital Data8

9.  Convert the decimal value 150 to binary  What decimal value does the bit pattern  1 1 0 1 0 0 1 0 0  Convert the binary pattern 1 0 0 1 0 1 1 1 0 0 0 1  To hex Digital Data9

10.  Convert 2017 to binary (base 2)  Convert 2017 to hexadecimal (base 16) 7 / 16 =0remainder 7 126 / 16 =7remainder e (14) 2,017 / 16 =126Remainder 1 Digital Data 10 1 / 2 =0remainder 1 3 / 2 =1remainder 1 7 / 2 =3remainder 1 15 / 2 =7remainder 1 31/ 2 =15remainder 1 63 / 2 =31remainder 1 126 / 2 =63remainder 0 252 / 2 =126remainder 0 504 / 2 =252remainder 0 1,008 / 2 =504remainder 0 2,017 / 2 =1,008remainder 1 Binary Digits Left to Right 2017 10 = 11111100001 2 2017 10 = 7e1 16 Hex Digits Left to Right Convert 11111100001 to hex Simple: Break up the Binary number into sets of four bits 0111 1110 0001 Look at Binary-Hex chart 7 e 1

11.  American Standard Code for Information Interchange (ASCII)  Character-encoding scheme based on the ordering of the English alphabet  Maps digital bit pattern and character symbol  Includes  Printable characters  Alphabet, numbers, symbols  Graphics characters  ■ ┌ ┐ ╔ ╗  Control characters  Backspace, tab, line feed, carriage return  Many of these characters are non-printable Digital Data11

12. Digital Data12

13.  Strings are a sequence of bytes  Bytes represent ASCII characters  Characters can be represented as  Character value: ‘m’  Decimal value: 109  Binary value: 0110 1101  Hexadecimal value: 6d  Try entering these URLs in a browser  http://google.com  http://%67%6f%6f%67%6c%65%2e%63%6f%6d  ‘%’ tells the program what follows is a hex value Digital Data13

14.  A file is a collection of binary data  Format determines the interpretation of bit patterns  Specifies the type of data a file contains  Text, image, sound, Word, Excel, etc.  Example  01010101 01010011 01000001  USA (ASCII text file)  (24-bit bitmap) Digital Data14

15.  Executable programs are just files  Sequence of bytes  Computers interpret the byte sequence as instructions  Executable file formats  Windows – Portable Executable (PE) format .exe,.dll (libraries),.sys (device drivers)  UNIX – Executable and Linkable Format (ELF)  Also used by UNIX variants  Linux, BSD, Solaris  Mac OS X – Mach object file (Mach-O)  Earlier Mac OSs use Preferred Executable Format (PEF) Digital Data15

16.  Convention for naming files .  Extension is usually three letters .txt (text),.jpg (JPEG image),.mp3 (MP3 audio),.doc (Word),.xls (Excel)  Can be more or less .c (C source code),.gz (GNU zip),.docx (Word),.xlsx (Excel)  Extension DOES NOT determine bit interpretation  Determined by file format (ie., how file is being viewed)  Operating systems and applications make decisions based on file extension .doc *ought* to be a Word document…I should use Microsoft Word to open it  Extensions can be changed without changing the file format  Example: change.zip to.txt to email a ZIP file  Can still open the “.txt” file with a program that recognizes the ZIP file format Digital Data16

17.  What string is represented by the ASCII values : 85 83 77 67  What exactly is displayed when we open the file yay.txt in notepad which consists of the following bytes:  1010101 1010011 1001101 1000011 What exactly would be displayed in the hex editor Frhed when we open yay.txt? Digital Data17

18.  Number Systems Decoded http://www.globalknowledge.ca/articles/whitepaper detail.asp?wpid=315  RFC 20: ASCII format for Network Interchange http://tools.ietf.org/html/rfc20  File Signatures Table http://www.garykessler.net/library/file_sigs.html  Comparison of Executable File Formats http://en.wikipedia.org/wiki/Comparison_of_execut able_file_formats Digital Data18