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Introduction CS3402 Digital Logic Design Reading Assignment: Chapters 0 & 1 A. Berrached 1 Digital Hardware Systems Electronic systems: • Digital Systems vs. Analog systems • Digital vs. Analog Signals +5 +5 1 0 1 V V Time –5 Time –5 Digital: only assumes discrete values Analog: values vary over a broad range continuously A. Berrached 2 Digital Hardware Systems Advantages of Digital Systems • Analog systems: slight error in input yields large error in output • Digital systems are more accurate and reliable: can deal better with degraded signals • Digital signals are generally easier to process • Current general purpose computers are digital • Real life signals (e.g. human voice) are analog • Interface circuits (i.e. sensors & actuators) are often analog • Digital signals are generally used as an approximation to real analog signals A. Berrached 3 Binary Digital Systems +5 High Noise margin V Low 0 time • The simplest digital systems are binary digital systems – only two discrete values » easier to decode – rigorous mathematical foundation based on logic & Boolean algebra A. Berrached 4 Digital Hardware Systems Digital Binary Systems • Two discrete values: high voltage, high current flowing, ON, TRUE, YES, "1" low voltage, low current flowing, OFF, FALSE, NO, "0" • Advantage of binary systems: • rigorous mathematical foundation based on logic & Boolean Algebra • Math. Logic allows to reason about the truth of a set of statements IF( the garage door is open) AND ( the car is running) THEN the car can be backed out of the garage • “the garage door is open”, “the car is running”, “the car can be backed out of the garage” are logical propositions that can be TRUE or FALSE. • AND is a logical operator: The two preconditions must be True for the conclusion to be true A. Berrached 5 Digital Hardware Systems • Boolean Algebra – Deals with logical propositions/statements and their logic values: A logical statement can be either TRUE or FALSE ( 0 or 1). – provides algebraic formulation of how to combine logic values. » Logic operators • At the hardware level: – Each logical statements is represented with an electrical signal. – The logic value of a statement is represented with the signal’s voltage level Example: High voltage level => Statement is True Low voltage level => Statement is False – Logic operators are represented with Logic Gates A. Berrached 6 Digital Hardware Systems Boolean Algebra and Logical Operators Three basic Logical Operations: AND, OR, NOT X Y X AND Y F F T T F T F T F F F T X Y Low Low High High X Y X AND Y X 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 Y 0 1 0 1 Low High Low High X OR Y 0 1 1 1 X AND Y Low Low Low High X NOT X 0 1 1 0 Any Boolean function can be realized using AND, OR and NOT A. Berrached 7 Digital Hardware Systems Hardware Systems and Logical Operators IF the garage door is open AND the car is running THEN the car can be backed out of the garage door open? Low/0 Low/0 High/1 High1 car running? Low/0 High/1 Low/0 High/1 Door Open back out car? Low/0 Low/0 Low/0 High/1 Back out car Car running AND gate A. Berrached 8 Digital Hardware Systems • Logic gates are the standard building blocks used to build primitive logic operations • Digital Technologies: • Electron Tube technology – Electron tubes, resistors and capacitors – interconnected with copper wire • Discrete Transistor technology • Resistor-Transistor Logic (RTL) • Diode-Transistor Logic (DTL) A. Berrached 9 Integrated Circuits (ICs) • Integrated circuit technology » Uses conducting, non-conducting, and semi-conducting (i.e. “sometimes conducting” ) materials » the basic component: Transistor (electrically controlled switch) » An Integrated Circuit (IC): a device (a chip) that contains from few to several million transistors => Small size, low power consumption, high speed A. Berrached 10 Integrated Circuits (ICs) Two Main IC Technologies: • Bipolar – Transistor-Transistor Logic(TTL): Medium Power Consumption, Medium Speed • SSI, MSI – Emitter Coupled Logic (ECL): High Power Consumption, High Speed • SSI, MSI, LSI • CMOS:Complementary Metal-Oxide-Silicon Low Power Consumption, Medium Speed • VLSI A. Berrached 11 Integrated Circuits (ICs) • Scales of integration – Small Scale integrated Circuits (SSI) » ICs with 1 to 10 gates » Independents gates – Medium Scale integrated Circuits (MSI) » ICs with 10 to 100 gates » IC performs one standard function (e.g. decoder, Multiplexer, counter, adder, etc.) – Large Scale integrated Circuits (LSI) » ICs with 100 to 1000s of gates » IC performance relatively complex functions (e.g. an ALU, a memory device, etc.) – Very-Large Scale integrated Circuits (VLSI) » Ics with 1000s to millions of gates » Processors, Memories, etc. A. Berrached » CMOS technology 12 Digital Hardware Systems CMOS Technology Transistor : basic electrical switch Gate Drain Sourc e three terminal switch: gate, source, drain when voltage between gate and source exceeds a certain threshold the switch is conducting or "closed" => electrons flow between source and drain when voltage is removed, the switch is "open" or non-conducting => connection between source and drain is broken Control A. Berrached Switch 13 Digital Hardware Systems : Switches A transistor can be represented as a switch A switch connects two points under a control signal. Normally Open when the control signal is 0 (false), the switch is open when it is 1 (true), the switch is closed Normally Closed when control is 1 (true), switch is open when control is 0 (false), switch is closed True Control Closed Switch True Control False Normally Open Switch Open Switch False Normally Closed Switch Open Switch A. Berrached Closed Switch 14 Implementation of AND and OR Functions with Switches A B The output is True if and only if False A AND B are True. output => this circuit realizes the AND function True Abstract Representation: A OR Output B AND gate A. Berrached 15 Implementation of AND and OR Functions with Switches A B False Output is True iff A is True OR B is True (or both are True) output => The circuit realizes the OR function True Abstract Representation: A Output B OR gate A. Berrached 16 • Semi-conductor material => Transistors • Transistors => Logic Gates • Gates => any switching function – Arithmetic: Adders, Multipliers, Dividers, etc. – Logic » ALU – Storage Devices: registers, memory – Control Devices A. Berrached 17 Digital Systems Design Hierarchy System-level microprocessors, storage units, buses. Register-level registers, adders, multipliers, control units, etc. Gate-level AND, OR, NOT, EX-OR gates counters, multiplexers, decoders, laches, etc. Transistor-level Transistors, diodes, resistors, capacitors, etc. This course is about logic design, not system design (processor A. Berrached architecture), not circuit design (transistor level) 18 Course Coverage • Binary Number Systems and Codes • Boolean Algebra • Analysis, Synthesis, and implementation of Combinational Circuits • Analysis, Synthesis, and implementation of Sequential Circuits A. Berrached 19