Chapter 3Chapter 3Digital Logich d k b h b fWhat you need to know about the basic components of computingDevices: TransistorDevices: Transistor‐‐LevelLevelVccVoutVinVoutRcRbVOHminVccoutAbnormal fz Vinlow → Ib= 0GNDVinVOLmaxVCESatexcept for switchinginb–transistor cut off: Vout= Vccz Vinhigh → Ib> 0–transistor “on”: Vout= GNDVccVIHminVOLmaxinGNDVOLmax: max output voltage in low state Vi t t lt i hi h t ttransistor on :VoutGNVOHmin: min output voltage in high state VILmax: max input voltage recognized as low VIHmin: min input voltage recognized as high2Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblyIHminpgg gDealing with complexityDealing with complexityz Transistors are hard to work/design withz When engineers encounter complexity, we preconstruct useful devices g py,pand focus on providing a general interface–This is abstractionzThe user need not know the details of the device implementationThe user need not know the details of the device implementation– Sometimes referred to as encapsulationz We then attempt to break down large problems into smaller problems for which we have already constructed solutions.for which we have already constructed solutions.–This is sometimes referred to as divide and conquer3Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblyComplex logic circuitsComplex logic circuitsz Logic circuits divide into two major types:z Combinational Logic– Current output depends on current input only–Examples: gates, decoders, multiplexors (MUXs), ALUs+mnDesign:avg (w,x,y,z)z Sequential Logic*p p * (m + n)a2+2ab+b2– Current output depends on past inputs as well as current input– Thus has a memory (usually called the state)–Examples: latches, flip‐flops, state machines, counters, registers4Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblyCircuits: GateCircuits: Gate‐‐LevelLevelz AND gate–Output Z = 1 only when inputs A and B are both 1AZz OR gate–Output Z = 1 only when inputs A or B or both are 1BZAz NOT gate or inverter– Output Z = 1 only when input A is 0ABZzAll of computing is made up of a few very basic operations like ANDZAzAll of computing is made up of a few very basic operations like AND, OR, and NOT– Simple alone, but combine a few million gates properly and you have a computer!5Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblypCircuits: a MultiplexorCircuits: a MultiplexorWith 16 of these, In1In2In3In4A four‐input MUXIn1In2In3In4we can build a 16‐bit four input MUX16S0S1S0S116Out Out166Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblyCircuits: an ALUCircuits: an ALUABNote that this is a Note that this is a 16A16BNote that this is a Note that this is a combinationalcombinational device: device: it has no memory.it has no memory.AddSubMulDiIf you want to see the If you want to see the result on the Out line, result on the Out line, you must you must continuously supply continuously supply PNZV16Divcontinuously supply continuously supply operands on A and B, operands on A and B, and one (and only and one (and only one) operation one) operation Outselector.selector.7Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblyKeeping track of stateKeeping track of statez Suppose we perform an addition (A + B) on our ALU. Where can we “”h l?“put” the result?–We need a place to save the answer so that we can use it for the next operationC il th lt bkit th A B it?zCan we simply run the result back into the A or B input?16A16B161616AddSubMulDivWhy is this a bad idea?16Out8Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblyCircuits: A Circuits: A bistablebistable elementelement292.9 vOutDQClkQ9Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblyCircuits: a Register Circuits: a Register CLKDQ0QD0REG 4OUTINQDQD144Q1OUTINDQD1DQD2Q2LoadDQD2DQ3QD3If R0 is 0011 (x3)ThenQDQCLKR0[3:0] is 0011 R0[2:0] is 011R0[2:1] is 01R0[0:0] is 110Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblyR0[0:0] is 1Computation + storageComputation + storage16A16B16‐bit registerClk16‐bit registerAddSub16MulDiv16‐bit register11Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblyPractice ProblemsPractice Problemsz 3.3, 3.9, 3.14, 3.29, 3.31z 3.25 with the following correction: the propagation delay of figure 3.11 is 1.12Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. & AssemblyBusses and Drivers (the triBusses and Drivers (the tri‐‐state buffer)state buffer)13Wright State University, College of EngineeringDr. Doom, Computer Science & EngineeringCEG 320/520Comp. Org. &