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What is a computer? A computer is a device that: – Accepts input – Processes data – Stores data – Produces output Let’s examine components in more detail… What is a computer? A computer is a device that: – Accepts input: Input devices Name as many as you can: What is a computer? A computer is a device that: – Accepts input: Input devices Name as many as you can: Keyboard, mouse, scanner, bar code reader, light pen, infrared sensor, video camera and many more… What is a computer? A computer is a device that: – Processes data: Processors Name as many as you can: What is a computer? A computer is a device that: – Processes data: Processors Name as many as you can: CPU, graphics processor, video controller, modem, and many more… What is a computer? A computer is a device that: – Stores data: Storage devices Name as many as you can: What is a computer? A computer is a device that: – Stores data: Storage devices Name as many as you can: Main memory, hard drive, CD-ROM, DVD-ROM, memory card, tape drive, ZIP disk, floppy disk, What is a computer? A computer is a device that: – Produces output: Output devices Name as many as you can: What is a computer? A computer is a device that: – Produces output: Output devices Name as many as you can: Monitor, printer, speaker, indicator light, and many more… Data Representation A computer is a device that: – Accepts input – Processes data – Stores data – Produces output Input data transformed into output. Data can be stored for Data Representation Spreadsheet data graphs 3D models animation Vocals and MIDI Song Bar code Price of item Card and Pin # Money Data Representation How can we represent information in a way that can be stored and manipulated by a computer? Data Representation and Storage External representation: computers use decimal digits (base ten), 26character alphabet for easier human interaction via keyboard, terminal, printer Internal representation: computers use binary system for numbers, letters, graphics, etc. Data Representation Internally, computers represent information as patterns of bits A bit (binary digit) is either 0 or 1; these are symbols and have no numeric meaning Storing a bit requires that a device can be in one (and only one) of just two states; analogous to true and false Bit Storage Why only two states? Why not use ten states to correspond with the base ten numbering system? Data Representation Binary Numbers!!! Sound pitch number binary number Letter number binary number Image color at each pixel number binary number Decimal Number Systems Base 10 Digits - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 e.g. 34210 = = 3 x 102 + 4 x 101 + 2 x100 = 3 x 100 + 4 x 10 + 2 x 1 = 300 + 40 +2 Binary Number System Base 2 Digits 0, 1 e.g. 1102 = = 1 x 22 + 1 x 21 + 0 x 20 = 1x4 +1x2 +0x1 = 4 +2 +0 = 6 Counting in Binary Decimal 0 1 2 3 4 5 Binary 0 1 10 11 100 101 Decimal 6 7 8 9 10 11 Binary 110 111 1000 1001 1010 1011 Place and value In a decimal number, each place value is 10 times greater than the place to its right. In a binary number, each place value is 2 times greater than the place to its right. For convenience, we group every four binary bits into a hexdecimal digit (1-9, A,B,C,D,E,F) In a hexdecimal number, each place value is 16 times greater than the place to its right. Binary Numerals 01101101 – Bits are numbered from the right b7 b6b5b4b3b2b1b0 – Subscripts represent the place value bi has place value 2i – Convert to decimal b7 * 27+b6*26 + b5*25 +b4*24 +b3*23 +b2*22 +b1*21 + b0*20 Data Representation 100 = 1 * 22 + 0 * 21 + 0 10 = 1 * 21 + 0 1 Data Representation Binary to Decimal 10011 = 1 * 24 + 0 * 23 + 0 * 22 + 1* 21 + 1 * 20 Data Representation Binary to Decimal 10011 = 1 * 24 + 0 * 23 + 0 * 22 + 1* 21 + 1 * 20 = 16 +0 +0 + 2 +1 = 19 Excercise 1011b = ?d Addition 1000 + 1 =? 0011 + 0010 = 4 bits and Hex – 0000 ;0 – 1000 ;8 – 0001 ;1 – 1001 ;9 – 0010 ;2 – 1010 ;10 (Ah) – 0011 ;3 – 1011 ;11 (Bh) – 0100 ;4 – 1100 ;12 (Ch) – 0101 ;5 – 1101 ;13 (Dh) – 0110 ;6 – 1110 ;14 (Eh) – 0111 ;7 – 1111 ;15 (Fh) Converting Binary to Decimal Another method: repeatedly multiply by 2 and add next bit e.g. 110101 0x2= 0+1= 1 1x2= 2+1= 3 3x2= 6+0= 6 6 x 2 = 12 + 1 = 13 13 x 2 = 26 + 0 = 26 26 x 2 = 52 + 1 = 53 Converting Decimal to Binary Repeatedly divide by 2, recording remainders in reverse order e.g. 53 / 2 = 26 R 1 26 / 2 = 13 R 0 13 / 2 = 6 R 1 6/2= 3R0 3/2= 1R1 1/2= 0R1 giving 110101 Data Representation use a fixed number of digits. But how many bits do we need? 1 binary digit 2 binary digits 3 binary digits 101, 110, 111 0 or 1 2 possible chars 00, 01, 10, 11 4 chars 000, 001, 010, 011, 100, 8 chars Data Representation Solution: use a fixed number of digits. But how many bits do we need? 1 binary digit 0 or 1 2 possible chars 2 binary digits 00, 01, 10, 11 4 chars 3 binary digits 000, 001, 010, 011, 100, 101, 110, 111 8 chars Notice a pattern? 12, 24, 38, … the total number of character that can be represented by n bits is 2n Number of bits How many states can be represented with 1 bits, 2 bits, 3 bits, 8 bits …. To represent N states, how many bits are needed. Data Representation But how many bits are needed to store n symbols? Or, how many bits are needed to represent n numbers? log2n Character Representation 1 byte = 8 bits = 1 character? 256 possible codes with 8 bits Assign a character to each code Common assignment – ASCII - American Standard Code for Information Interchange – defines first 128 ASCII Code Code Value Letter 0 Null character 1 - 31 Special Control Characters 10 \n = New line 32 Space 33-47, 58-64, 91-96 Punctuation 48 - 57 0-9 65 - 90 A-Z Interesting ASCII Choice? Digits 0 through 9 seem strange? Digit Dec Hex 0 48 30 1 49 31 … … … 9 57 39 Data Representation American Standard Code for Information Interchange (ASCII ) defines 256 symbols that can be stored in a byte. Each symbol corresponds to a number from Symbol Decimal Binary 0 -- 255 @ 64 01000000 A 65 01000001 B 66 01000010 C 67 01000011 D 68 01000100 E 69 01000101 F 70 01000110 G 71 01000111 H 72 01001000 Unicode International language coding standard Superset of ASCII Various codes defined to use upper 128 bits for symbols and other languages Memory Sizes Byte = 8 bits Kilobyte (K) = 210 = 1,024 bytes Megabyte (Mb) = 220 = 1,048,576 bytes Gigabyte (Gb) = 230 = 1,073,741,824 bytes 16-bit Memory Word To store number 6, use 0000000000000110 Value 0 is 0000000000000000 Largest value is 1111111111111111 = 65,535 = 216 − 1