Introduction to Digital SystemsAdvantages of Digital Systems Over Analog SystemsBoolean AlgebraSlide 4Digital (logic) Elements: GatesLogic GatesTruth TablesRealizing Logic in HardwareLogic Gates: The InverterLogic Gates: The AND GateCircuit to determine AND Gate Truth Table (From Lab 1)Logic Gates: The OR GateLogic Gates: The NAND GateLogic Gates: The NOR GateLogic Gates: The XOR GateDrawing Logic CircuitsAnalysing Logic CircuitsAnalysing Logic CircuitSimple Circuit Design: Two-input MultiplexerIntegrated CircuitsComputer Hardware GenerationsHierarchy of Computer ArchitectureA Hierarchy of Computer DesignEECC341 - ShaabanEECC341 - Shaaban#1 Lec # 1 Winter 2001 12-4-2001Introduction to Digital Systems•Analog devices and systems process time-varying signals that can take on any value across a continuous range.•Digital systems use digital circuits that process digital signals which can take on one of two values, we call: 0 and 1 (digits of the binary number system) or LOW and HIGH or FALSE and TRUE•Digital computers represent the most common digital systems.•Once-analog Systems that use digital systems today:–Audio recording (CDs, DAT, mp3) – Phone system switching–Automobile engine control –Movie effects–Still and video cameras….HighLowDigital circuitinputs outputs: :Analog SignalDigital SignalEECC341 - ShaabanEECC341 - Shaaban#2 Lec # 1 Winter 2001 12-4-2001Advantages of Digital Systems Over Analog Systems•Reproducibility of the results and accuracy.•More reliable than analog systems due to better immunity to noise. •Ease of design: No special math skills needed to visualize the behavior of small digital (logic) circuits.•Flexibility and functionality.•Programmability.•Speed: A digital logic element can produce an output in less than 10 nanoseconds (10-8 seconds).•Economy: Due to the integration of millions of digital logic elements on a single miniature chip forming low cost integrated circuit (ICs).EECC341 - ShaabanEECC341 - Shaaban#3 Lec # 1 Winter 2001 12-4-2001Boolean AlgebraBoolean Algebra•Boolean Algebra named after George Boole who used it to study human logical reasoning – calculus of proposition.•Elements : true or false ( 0, 1)•Operations: a OR b; a AND b, NOT a e.g. 0 OR 1 = 1 0 OR 0 = 0 1 AND 1 = 1 1 AND 0 = 0 NOT 0 = 1 NOT 1 = 0What is an Algebra? (e.g. algebra of integers)set of elements (e.g. 0,1,2,..)set of operations (e.g. +, -, *,..)postulates/axioms (e.g. 0+x=x,..)EECC341 - ShaabanEECC341 - Shaaban#4 Lec # 1 Winter 2001 12-4-2001Boolean AlgebraBoolean Algebra•Set of Elements: {0,1}•Set of Operations: {., + , ¬ }Signals: High = 5V = 1; Low = 0V = 0x y x . y0 0 00 1 01 0 01 1 1x y x + y0 0 00 1 11 0 11 1 1x ¬x0 11 0xyx.yxyx+yxx'Sometimes denoted by ’, for example a’ANDORNOTEECC341 - ShaabanEECC341 - Shaaban#5 Lec # 1 Winter 2001 12-4-2001Digital (logic) Elements: Gates•Digital devices or gates have one or more inputs and produce an output that is a function of the current input value(s).•All inputs and outputs are binary and can only take the values 0 or 1•A gate is called a combinational circuit because the output only depends on the current input combination. •Digital circuits are created by using a number of connected gates such as the output of a gate is connected to to the input of one or more gates in such a way to achieve specific outputs for input values. •Digital or logic design is concerned with the design of such circuits.EECC341 - ShaabanEECC341 - Shaaban#6 Lec # 1 Winter 2001 12-4-2001Logic GatesLogic GatesEXCLUSIVE ORaba.baba+ba a'ab(a+b)'ab(a.b)'aba  baba.b&aba+b1ANDa a'1ab(a.b)'&ab(a+b)'1aba  b=1ORNOTNANDNORSymbol set 1Symbol set 2(ANSI/IEEE Standard 91-1984)EECC341 - ShaabanEECC341 - Shaaban#7 Lec # 1 Winter 2001 12-4-2001Truth Tables•Provides a listing of every possible combination of values of binary inputs to a digital circuit and the corresponding outputs.x y x . y x + y0 0 0 00 1 0 11 0 0 11 1 1 1INPUTS OUTPUTS… …… …•Example (2 inputs, 2 outputs):Digital circuitinputsoutputsxyinputsoutputsx + yx . yTruth tableEECC341 - ShaabanEECC341 - Shaaban#8 Lec # 1 Winter 2001 12-4-2001Realizing Logic in Hardware•Boolean Algebra and truth tables are essential important tools to express logical relationships.•To use these tools in the real world , we must have some physical way to represent TRUE and FALSE (T and F).•In, digital electronic circuits, T and F are represented by voltage levels: –The transistor-transistor logic (TTL) 74LS family of digital integrated circuits produces two voltage levels:• < .5V which represents low voltage L (0) and,•> 2.7V which represents high voltage H (1) for the digital device.EECC341 - ShaabanEECC341 - Shaaban#9 Lec # 1 Winter 2001 12-4-2001Logic Gates: The InverterLogic Gates: The Inverter•The InverterA A'0 11 0A A' A A'1 2 3 4 5 6 7891011121314GroundVccTop View of a TTL 74LS family 74LS04 Hex Inverter IC PackageTruth tableEECC341 - ShaabanEECC341 - Shaaban#10 Lec # 1 Winter 2001 12-4-2001Logic Gates: The AND GateLogic Gates: The AND GateA B A . B0 0 00 1 01 0 01 1 1ABA.BTruth table1 2 3 4 5 6 7891011121314GroundVccTop View of a TTL 74LS family 74LS08 Quad 2-input AND Gate IC Package•The AND GateEECC341 - ShaabanEECC341 - Shaaban#11 Lec # 1 Winter 2001 12-4-2001Circuit to determine AND Gate Truth Table(From Lab 1) 750 ohm123U1A74LS081 2U2A74LS04750 ohm750 ohmD1LEDS1S2Vcc Vcc VccVa VbVfEECC341 - ShaabanEECC341 - Shaaban#12 Lec # 1 Winter 2001 12-4-2001Logic Gates: The OR GateLogic Gates: The OR GateABA+BA B A + B0 0 00 1 11 0 11 1 1•The OR GateTruth tableTop View of a TTL 74LS family 74LS08 Quad 2-input OR Gate IC PackageEECC341 - ShaabanEECC341 - Shaaban#13 Lec # 1 Winter 2001 12-4-2001Logic Gates: The NAND GateLogic Gates: The NAND Gate•The NAND GateAB(A.B)'AB(A.B)'A B (A.B)'0 0 10 1 11 0 11 1 0Truth tableTop View of a TTL 74LS family 74LS00 Quad 2-input NAND Gate IC Package•NAND gate is self-sufficient (can build any logic circuit with it).•Can be used to implement AND/OR/NOT.•Implementing an inverter using NAND gate:x x'EECC341 - ShaabanEECC341 - Shaaban#14 Lec # 1 Winter 2001 12-4-2001Logic Gates: The NOR GateLogic Gates: The NOR Gate•The NOR GateAB(A+B)'AB(A+B)'A B (A+B)'0 0 10 1 01 0 01 1 0Truth