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Computer System

Computer System. Building blocks of a computer system: Using bits Binary data and operations Logic gates Units of measuring amount of data CPU vs. memory ( Operating System) Programming languages  Models of computation, e.g. Turing Machine. Binary.

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Computer System

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  1. Computer System • Building blocks of a computer system: • Using bits • Binary data and operations • Logic gates • Units of measuring amount of data • CPU vs. memory • (Operating System) • Programming languages  • Models of computation, e.g. Turing Machine

  2. Binary • All information inside computer is in binary • Smallest unit of data is the bit • Only the values 0 and 1 are used 0 means “false” or “off” or the number 0 1 means “true” or “on” or the number 1 • Individual bit values can be manipulated with Boolean operations: “and”, “or”, “not”, etc. • In hardware, we implement these operations with logic gates.

  3. Boolean examples • AND • To graduate, you must have 128 credits and 2.0 GPA. • OR • Classics scholarship requires 3 years of Latin or 3 years of Greek. • XOR (“exclusive” or) • To go to Cincinnati, you can fly or drive. In other words, it doesn’t make sense to do both. • Do you want a 2-door or a 4-door car? • NOT • If a statement is true, its negation is false, and vice versa.

  4. Gates • Basic building blocks of CPU’s circuitry. • Usually 2 inputs. • X and Y could be 0 or 1. • Combining gates into a circuit: • The output of one gate becomes input to another. • This is how more useful operations are performed.

  5. ‘AND’ and ‘OR’ Note: 0 AND (anything) = 0 1 OR (anything) = 1

  6. XOR • XOR basically says, “either but not both” • The output is 1 if both inputs are different.

  7. NOR, NAND • NOR gate • Negation of the OR • Same as feeding output of OR into a NOT gate. • Symbol for NOR gate is same as OR but with a loop on the end. • NAND gate • Negation of the AND…. analogous to NOR. • Interesting property: • NOR and NAND are universal gates. Any other boolean operation can be implemented by using several NAND’s or several NOR’s.

  8. Units of data size • Bit = a single 0 or 1 value • Nibble = 4 bits = 1 hexadecimal digit • Byte = 8 bits • Kilobyte (KB) = 210 bytes • Megabyte (MB) = 220 bytes • Gigabyte (GB) = 230 bytes • Terabyte (TB) = 240 bytes • 210 = 1024, though 1000 is a close approx.

  9. CPU and memory • CPU’s job is to obey instructions and do calculations • Memory system stores information for current and future use • CPU has tiny number of “registers” for calculations • main memory (RAM) stores all files currently open • Secondary memory (e.g. hard drive) is for long-term storage of files • Backup system: tape, external hard drive • Other types of memory: • Cache, between CPU and RAM • Removable drive, e.g. USB or DVD

  10. RAM • Runs on electricity: volatile but fast • Each byte is numbered and addressable • Capable of holding a single character or small #

  11. CPU, memory • Contrast between levels of memory • Tradeoff between cost / size / speed • Manipulating data by performing instructions • “What is going on in the CPU?” • Handout • A simple machine language

  12. Memory comparison Numbers are approximate. “ns” means nanosecond = 1 billionth of a second

  13. Basic computer anatomy • Inside a computer are 2 parts • CPU • Memory • These are connected by a data bus: an “HOV lane” where traffic can go either way. • CPU contains: • ALU: arithmetic and logic unit • Control unit: figures out what to do next • Registers to hold values needed for calculation • Memory (RAM) contains: • Software: list of instructions the CPU needs to perform • Data: Input and output values need to be stored while program runs

  14. Stored program idea • Program = software = list of instructions for CPU to do • Programs reside in memory • CPU will do 1 instruction at a time • For each instruction, we do the following: • Fetch it from memory • Decode – figure out what it means • Execute – do it • And then we continue with the next instruction… until the program is finished.

  15. Simple example • A program to add two numbers. • This program may reside at bytes 100-116 in RAM. • The two numbers we wish to add are located at bytes 200 and 204 in RAM. • We want the result to go into memory at byte 208. • Program may go something like this: • Load the value at Memory[200] into register 1. • Load the value at Memory[204] into register 2. • Add registers 1 and 2, and put result in register 3. • Store the value from register 3 into Memory[208]. • Note that the bus is communicating instructions (RAM to CPU) as well as data (both ways).

  16. Machine language • Unfortunately, instructions for CPU can’t be in English, French, etc. • Machine language = binary (or hex) representation of our instructions. • Each type of computer has its own machine language. • This is the original form of “computer programming”. • Verbs: Instruction set. e.g. Add, subtract, load, store… • Nouns: Operands such as: registers, memory locations, constants, other instructions

  17. Verbs 3 kinds of instructions (instruction set) • Data transfer, using the bus • Load a value from memory into a CPU register Very similar to fetching an instruction! • Store a value from a CPU register into memory • ALU • Bit manipulation: AND, OR, XOR, NOT, shift left, shift right, … • Arithmetic: add, sub, mul, div, remainder, =, <, >, , , ≠, … • Control • “Go to” another instruction in program. In other words, interrupt normal sequence of instructions. • Can be conditional or unconditional

  18. Example language • Let’s consider very simple HW. • 256 bytes of RAM: addressable by 8 bits • CPU contains • Instruction register (to store contents of instruction) • Program counter (to indicate instruction’s address) • 16 general purpose registers: addressable by 4 bits • Each register is 1 byte • Each instruction is 2 bytes = 16 bits = 4 hex digits long • Instruction format: • First 4 bits are the opcode = specify which instruction type • Other 12 bits are operand(s) • What do instructions mean?

  19. Machine language • Machine language examples • Don’t memorize… • Instruction execution • Operations in instruction set • Performing arithmetic sometimes requires load / store instructions in addition to the arithmetic instruction • Instructions to manipulate bits directly

  20. Example instructions • Note: 16 possible opcodes: 4 bit opcode • Note: 16 possible registers: register number also 4 bits • Opcode 5 is used for adding • Expects 3 register operands • 5RST means R = S + T, where R, S and T are register numbers • Ex. 5123 means Add registers 2 and 3 and put result in register 1. • Opcode 2 is for putting a constant in a register • Expects a register operand, and an 8-bit constant operand • 2RXX means R = XX, where XX is some 8-bit pattern • Ex. 27c9 means Put the hexidecimal “c9” into register 7. • Try an example using both types of instructions.

  21. More instructions • Opcode 1 is for loading a memory value into a register • Expects a register operand (4 bits), and a memory address from which to load (8 bits). • Ex. 1820 means to go out to memory at address [20], grab the contents and load it into register 8. (It does not mean put the number 20 in register 8.) • Opcode 3 is a store = opposite of load • Ex. 3921 means to take the value in register 9, and put it into memory at location [21]. (It does not mean put the number 9 into memory location 21.) • Opcode C (hex code for 12) is for telling CPU it’s done. • Expects operand to be 12 zero-bits.

  22. Instruction format • How many bits do we need to specify: • One entire instruction? • Its operation, a register, or a memory address? • On real machines, 32 bits is a convenient size for: • Numbers (integer and real) • Memory address • Instruction • Therefore, size of each register is 32 bits • Research: 32 registers is enough for CPU • Example in handout refers to much smaller machine

  23. Comparison

  24. Some practice Refer to handout… • How would we put the number 64 into memory at address 12? • How would we add the numbers 6 and 8 and put the result in register 1? • How would we add register 7 to register 5 and put the answer in memory at address 32?

  25. Execution • In our example, each instruction is 2 bytes long. • Program counter (PC) begins at address of first instruction. • For each instruction: • Fetch (and increment PC by 2) • Decode • Execute • Note that RAM contains both instructions and data, separated from each other. For example, addresses 0-99 could be reserved for code.

  26. Bitwise • Operations that manipulate bits directly • Logical • Shift

  27. Logic operations • Work just like gates, but we do several bits in parallel. • Examples 10101110 01101011 AND 11110000 AND 00011111 • Try the same examples with “OR” and “XOR” • Observations: • What happens when you AND with a 1? With a 0? • What about OR’ing with a 1 versus a 0? • What about XOR? • ASCII code: how do you capitalize a letter?

  28. Shift operations • Given a bit pattern like 00011100, we can shift the bits left to obtain: 00111000. • If we shift to the right instead, 00011100 becomes this: 00001110. • We can even shift by more than one position. • Shifting 01010000 by 3 bits right  00001010. • Sometimes when we shift, 1’s fall off the edge. • Shifting 01010000 by 2 bits left  01000000. • When we shift, the “vacated” bits are usually 0.

  29. Why shift? • One application of a shift operation is to: • Multiply by 2: left shift • Divide by 2: right shift • Try some examples – should look familiar with our earlier work on binary numbers. • One funny exception: dividing a (signed) negative number by 2. We need a different operation: arithmetic right shift. • In this case, we want the vacated bit to be 1 • Example: –12 in signed is 11110100. If we shift right by 1, we get 01111010, but it should be this: 11111010.

  30. Rotate • Rotate operations work the same as shift… except that the vacated bits come from the other end of the number. • So, instead of 1’s falling off the edge, they rotate. • For example, 01010000 rotated left by 2 becomes 01000001. • Also: 00001111 rotated right by 3 becomes: 11100001.

  31. Summary • Here is a list of bitwise operators: • Logical • and, or, xor, not • Shift • sll (Shift left logical) • srl (Shift right logical) • sra (Shift right arithmetic) • rol (Rotate left) • ror (Rotate right)

  32. Language evolution • Machine language • Assembly language • Like machine language, also unique to each manufacturer • High-level language  • FORTRAN, COBOL • Pascal, Algol, Ada • C, C++, C# • Java, Javascript, Python • many more

  33. Example • How would we calculate: 12 + 22 + 32 + … + 202 ? • Let’s create our own solution, and see what the “code” looks like in different types of languages: • Machine language  • Assembly language  • High-level language 

  34. Machine language 00003000: 00000014 00004000: 200c0001 00004004: 20080000 00004008: 3c0a0000 0000400c: 354a3000 00004010: 8d4a0000 00004014: 018a4822 00004018: 1d200005 0000401c: 018c0018 00004020: 00005812 00004024: 010b4020 00004028: 218c0001 0000402c: 08001005 00004030: 2008000a 00004034: 0000000c help me!

  35. Assembly language numValue: .word 20 __start: addi $12, $0, 1 addi $8, $0, 0 lui $10, 0 ori $10, $10, 0x3000 lw $10, 0($10) while: sub $9, $12, $10 bgtz $3, end mult $12, $12 mflo $11 add $8, $8, $11 addi $12, $12, 1 j while end: addi $8, $0, 10 syscall

  36. HLL (Pascal) var sum : integer; count : integer; begin sum := 0; for count := 1 to 20 do sum := sum + count * count; writeln(sum); end.

  37. 3 ways to create code Write HLL code compiler Write assembly code assembler Write machine code Machine code Machine code

  38. What does a compiler do? • Scan • Break up program into tokens • Remove comments • Check syntax • Understand the structure of the program • Do all statements obey rules of language? • Generate code • Create appropriate machine/assembly instructions • Optimize operations to save time • We need a compiler for each language and architecture.

  39. Thinking • How computers think • Concept of “state” • Turing machine model • Finite state machine model a.k.a. “Finite automaton”

  40. State • Fundamental concept for any computation • Machine keeps track of where it is, what it needs • a.k.a. Status, mode • state may be stored in some memory cell • Many examples • Logging in • Using a dialog box, or other user-interface • Fax machine, photocopier, telephone • Car transmission

  41. Examples • In a Tic-Tac-Toe game, the “state” of the game would include: • Whose turn it is • Is the game over? Who won, or was it a tie? State is determined by looking at the board. • Backgammon (roll dice, move pieces…) • Depending on your situation in the game, some moves are illegal. • Another way to think about states is to consider all possible board configurations!

  42. Turing machine • Alan Turing, 1936 • Any general purpose machine must: • Work automatically • Be aware of what state it’s in • Have sufficient memory • Be able to do I/O, and be able to read the input many times if necessary • Powerful model, but tedious to work with

  43. Adder example S x y C z • 4 possible final states, depending on the inputs • For example, (S = 0 and C = 0) would be one outcome. • Programming the details make working with real TMs a headache.

  44. Finite Automatasingular: finite automaton Simple model for machine behavior. Purpose is to accept or reject some input Examples: logging in, using a wizard, game At any given time, machine is in some “state” Start state Final (or accept, “happy”) states Dead states Transitions between states

  45. Example Vending machine for 25¢ item. 0 5 10 +5 +5 +10 +10 +5 +25 25 20 15 +5 +5

  46. Binary example We want a “word” starting with “101…” need 101 1 need 01 0 need 1 1  1 0 0 0,1 

  47. What does this FA do? 1 A B 0 1 0

  48. Example We want a word with at least two 0’s. 0 need two need one 0  0,1 1 1 • What if we wanted exactly two 0’s?

  49. Regular language • Set of input strings that can be “accepted” or recognized by a FA. • Credit card numbers • Social security numbers • Phone numbers • Date / Time (e.g. to enter into reservation system) • Some FAs are too big to draw, so instead we describe with regular expression. • Shows general format of the input

  50. Regular expression • Use “wild cards” to make a general expression. • ? = can replace any single character • * = can replace any number of characters • [ ] = can hold a range of possible valid characters • Examples 105* = anything starting with 105 feb??.ppt= file names like feb25.ppt or feb04.ppt furman*.xlsx = any spreadsheet about Furman Version[123].txt = version1.txt, version2.txt, version3.txt

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