Final Review8/01/2007Topics Number systemsRepresent in various bases, convert between them, determine what base a number is in given decimal equivalentRepresent and work with signed numbers in all 3 formats we discussedAdd, subtract, multiplyTopics Boolean AlgebraBe able to reduce a boolean expression using boolean algebraBe able to derive equivalency between two expressionsYou’ll be given a listing of rules if neededTopics Karnaugh MapsBe able to use them to find MSP and MPS of some functionImplicants – Prime, EssentialDon’t Care’sTopics FunctionsBe able to represent them in all the formats we’ve discussed: truth table, sum of minterms, product of maxterms, boolean expression, etc.Be able to convert between these formatsBe able, given a description, to decide on the appropriate function(s)Topics GatesKnow and recognize all gate types we’ve discussed: AND, OR, NOT, NOR, NAND, XORBe able to implement a function as a circuit, convert it to all NAND or all NOR gatesBe able to deduce a function from a circuitTopics Decoders and MultiplexersRecognize block diagrams – active high/lowKnow how they functionUse them to implement a function(s)Again, be able to recover a function given a circuitTopics AddersKnow the difference between full/halfBe able to draw their internals (1-bit)Ripple-carry vs. carry lookahead vs. cascading carry lookaheadUse them to implement subtractionTopics ALUsModify inputs to adders to cause it to compute new functions.Determine which functions are implemented.Be sure which system you’re representing numbers inE.g. A-B in 1’s complement is A-B-1 in 2’s complement.Logical vs. Arithmetic. Bitwise vs. LogicalTopics LatchesCombinational vs. Sequential CircuitsBasic properties of memorySR latchS=1: set; R=1: reset SR=11: illegal inputTiming diagram;D latchControl/Data inputsTopics Flip FlopsClock edge triggered (positive or negative)Clock inputsD/JK/T flip-flops.Characteristic and excitation tables provided.Convert from one to anotherDirect (asynchronous) inputsTopics Sequential Circuit AnalysisBasically, determine what a circuit is doingConvert from a circuit to a state tableDetermine FF inputs, next states and outputsConvert from a state table to a state diagramTopics Sequential Circuit DesignGoing the other way: create a circuit to implement a specific deviceCreate a state diagram for some device (state recognizer, etc.) Convert a state diagram to a state tableConvert from a state table to a circuitMin. number of flip flops?TopicsCountersBe able to combine Counter-4’s to make larger countersAlter counting pathsStopping before reaching max valueStarting higher than 0Skipping values, etc.CO=0 when (UP=1 and value = 1111 orwhen UP =0 and value = 0000) and the counter is enabled.Create new counters from scratch (circuit design)Self-starting counterFrequency of a counterTopics Registers & Shift RegistersGrouping of conjoined Flip FlopsParallel load implementationShift left, shift rightCircular shiftsSwitch-tail ring countersMuxes to choose functionsTopicsRAMAddress lines for a size of ram.Each doubling in the address space adds 1 address line. Log2growth.Word size changes do not affect the number of address lines.Combine RAM chips to create larger RAM (both more address space and larger words)Use decoders to turn on/off proper chipsAddress ranges for chipsTopics Dynamic memory, ROMs, PLAsUnderstand the basic properties of ROMs and PLAsBe able to program ROMs and PLAs to implement functionsOr, read a pre-programmed ROM/PLA and give the function in some other formatAs part of the former, do PLA minimization via K-mapsTopics DatapathSet the control variables for the datapathto perform a specific operation, or read the control variables to determine what’s happeningDetermine if an operation can be performed (likely in one clock cycle) by a given datapathThe register transfer languageTopics Instruction Set ArchitecturesBe familiar with the assembly instructions we’ve discussedBe able to program basic operations in assembly, or extract functionality from codeConvert basic high-level constructs (loops, conditions) to assembly codeTopics Instruction Set EncodingBe familiar with our 3 formats: Register, immediate, and jump and branchPC-relative vs. Absolute jump/branch addressingConvert assembly instructions to machine language, vice versaWe’ll provide references for anything you needTopics Control Unit IntroductionUnderstand the various portions and how they’re interconnectedInstruction RAM/ROMProgram CounterInstruction DecoderBranch Control UnitBe able to generate any of the control variables from the machine languageTopics Other ISAsBe familiar with the various addressing types (what they mean and how to identify them)Be able to convert between instructions in 3-address, 2-address, 1-address and 0-addressRegister-to-register, memory-to-memory, and register-to-memory architecturesTopics Non-integer representationFixed-point numbersFloating-point numbersVarious properties and differences between
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