Logic Gates Part – III : Combinational Logic Gates Combinational Logic Circuits are made up from...

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Transcript of Logic Gates Part – III : Combinational Logic Gates Combinational Logic Circuits are made up from...

  • Logic GatesPart III : Combinational Logic Gates

    Combinational Logic Circuits are made up from basic logic NAND, NOR or NOT gates that are "combined" or connected together to produce more complicated switching circuits. Ex-OR and Ex-NOR gates are combinational gates. Course Name: Digital Logic Design Level(UG/PG): UG Author(s) : Phani Swathi ChittaMentor: Aruna Adil, Prof. C. Amarnath*The contents in this ppt are licensed under Creative Commons Attribution-NonCommercial-ShareAlike 2.5 India license

  • Learning ObjectivesAfter interacting with this Learning Object, the learner will be able to:Explain operations and applications of combinational logic gates

  • Definitions of the components/Keywords:53241 LOGIC: Reasoning conducted or assessed according to strict principles of validity.LOGIC GATE: The gate is a digital circuit with one or more inputs but only one output that can be activated by particular combinations of inputs.INPUT: The signal which is given to get the desired outputOUTPUT: Anything that comes outXOR GATE:The output is high (1) if its inputs are at opposite states. XNOR GATE: :The output is high (1) if its inputs are at same states. TRUTH TABLE : A truth table is a table that shows all the input-output possibilities of a logic circuit.LOGICAL EXPRESSION: A logical expression consists of one or more logical operators and logical, numeric, or relational operands.LOGICAL LAWS: laws which govern the logical circuits.

    The operation of a logic gate can be easily understood with the help of Truth Table.

  • Definitions of the components/Keywords:53241 Combinational Logic Circuits are made up from basic logic NAND, NOR or NOT gates that are "combined" or connected together to produce more complicated switching circuits. These logic gates are the building blocks of combinational logic circuits.The Ex-OR and Ex-NOR gates are combinational gates.The Ex-OR gate is an abbreviation for Exclusive-OR gate. It can also be written as XOR. Any combinational circuit can be implemented with only NAND and NOR gates.These gates are particularly useful in arithmetic operations as well as error-detection and correction circuits.

  • Boolean algebra is based on a number of properties that govern what manipulations can be performed on variables. The basic properties are shown below. For animator- below table must be shown after this statement Boolean variables can only take on one of two values, namely True and False. The values are called by different names. The most common pairs of names for True are {True, T, High, HI, H, 1} and the most common names for False are (False, F, Low, LO, L, 0}. In this LO, we use 0 and 1Definitions of the components/Keywords:53241

  • Definitions of the components/Keywords:53241Symbols and expressions used to represent logic gates:

    Ex - OR:

    This can be expressed as: X = A AND NOT B OR NOT A AND B

    Ex NOR:

    This can be expressed as: X = A AND B OR NOT A AND NOT BInput Output De Morgan's Theorems are one among the most powerful and useful theorems of Boolean Algebra. These theorems stem directly from the duality of Boolean logic and can be expressed as follows.

    A+B = AB

    AB = A+B

  • Description of the gates:

    Ex-OR: The XOR gate is a digital logic gate that produces a HIGH (1) output only when its inputs are at opposite states. A LOW(0) output occurs when inputs are same. The XOR operation is denoted with symbol +

    Definitions of the components/Keywords:53241

    Input 1Input 2OutputAB000011101110

  • Description of the gates: Ex-NOR: The XNOR gate is a digital logic gate that implements XOR function with a complemented (inverted) output. A LOW(0) output occurs when inputs are at opposite states. The gate produces a HIGH (1) output only when its inputs are same. Therefore XNOR gate is often referred to as the Equivalence gate. - It is also referred to as the coincidence operation because it produces the output of 1 when its inputs coincide in value; i.e., they are both 0 or both 1.- The XNOR operation is denoted with symbol

    A small circle or a bubble at the end of an XOR gate is used to signify the XNOR function.Definitions of the components/Keywords:53241

    Input 1Input 2OutputAB001010100111

  • Master Layout 53241 Give START, PAUSE and STOP buttons Give a slider to control the speed of animation Give a STEPPER button that allows the user to follow the simulation procedure step by step. After every step the simulation pauses until the STEPPER button is pressedGive a text area to display the status of the simulationFig. ASimulation Area GATE Menu XOR XNOR

    Seven radio buttons Basic concept of GATE Electronic Logic using Switches Applications of XOR Implementation of XOR using NAND Implementation of XOR using NOR Implementation of XNOR using NAND Implementation of XNOR using NOR

    Input AInput BOutputGATE SymbolTruth Table:Control Area10Legend: Toggle Switch1 - input is HIGH 0- input is LOW For XOR refer slide 10 72 For XNOR refer slide 73 124 Toggle Switch: a switch that has two positions . It has a mechanism to do two things one at a time**The demo itself is interactivity in this LO**

  • Step 1: 15324

    XORInput AInput BOutput10Legend:Truth Table:1 - input is HIGH 0- input is LOW

    Instruction for the animatorText to be displayed in the working area (DT)Initially only Gate menu is enabled and all other buttons are disabled (check slide 125 for more details)When user selects any Gate from Gate Menu, Show the respective gate symbol and display as it is shown in master layout fig. A Once XOR gate is selected, then enable/highlight five radio buttons basic concept of the gate, electronic logic, application of XOR, implementation of XOR using NAND and implementation of XOR using NORFollow the steps as shown in stepwise process. If basic concept of the GATE radio button is selected, the process should follow the steps shown from slide 10 18 If electronic logic is selected, the process should follow the steps shown from slide 19 27 If application of XOR is selected, the process should follow the steps shown from slide 28 41 If implementation of XOR using NAND is selected, the process should follow the steps shown from slide 42 55 If implementation of XOR using NOR is selected, the process should follow the steps shown from slide 56 72 The text in DT should appear in parallel to the figuresSelect Gate from Gate menu

    The 2-input XOR gate symbol and its truth table. 1 represents input HIGH 0 represents input LOW

    Input AInput BOutput

  • Step 2: 15324

    Basic concept of the XOR gateInput AInput BOutput0010Legend:

    Instruction for the animatorText to be displayed in the working area (DT) If basic concept of gate radio button is selected, the process should follow the steps shown from slide 10 - 18Initially show the figure in step 1, then highlight small grey squares in the switch and display 0 and 0 near the horizontal lines of the gate as shown Also show 0 and 0 in the truth table Then display 0 + 0 inside the gate The text in DT should appear in parallel to the figureInput A is 0 Input B is 0

    Input AInput BOutput00

  • Step 3: 15324

    Input AInput BOutput00010Legend:

    Instruction for the animatorText to be displayed in the working area (DT) Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureThe output is 0

    Input AInput BOutput000

  • Step 4: 15324

    Input AInput BOutput10Legend:01

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight grey square in the switch at input A and red square at input BDisplay inputs as 0 and 1 near the gate as shownAlso show 0 and 1 in the truth table as shown and keep filling the truth table along with old valuesThen display 0 + 1 inside the gate The text in DT should appear in parallel to the figureInput A is 0 Input B is 1

    Input AInput BOutput00001

  • Step 5: 15324

    Input AInput BOutput10Legend:101

    Instruction for the animatorText to be displayed in the working area (DT) Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureThe output is 1

    Input AInput BOutput000011

  • Step 6: 15324

    10Legend:Input AInput BOutput10

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight red square in the switch at input A and grey square at input BDisplay inputs as 1 and 0 near the gate as shownAlso show 1 and 0 in the truth table as shown and keep filling the truth table along with old valuesThen display 1 + 0 inside the gate The text in DT should appear in parallel to the figureInput A is 1 Input B is 0

    Input AInput BOutput00001110

  • Step 7: 15324

    10Legend:Input AInput BOutput110

    Instruction for the animatorText to be displayed in the working area (DT) Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureThe output is 1

    Input AInput BOutput000011101

  • Step 8: 15324

    10Legend:Input AInput BOutput11

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight red square in the switch at input A and red square at input BDisplay inputs as 1 and 1 near the gate as shownAlso show 1 and 1 in the truth table as shown and keep filling the truth table along with old valuesThen display 1 + 1 inside the gate The text in DT should appear in parallel to the figureInput A is 1Input B is 1

    Input AInput BOutput00001110111

  • Step 9: 15324

    10Legend:Input AInput BOutput011

    Instruction for the animatorText to be displayed in the working area (DT) Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureThe output is 0

    Select any radio button to view different ways of implementing XOR

    Input AInput BOutput000011101110

  • Step 10: 15324

    XOR gate using Switches10Legend:Input AInput BOutputUsing Electronic switchesLEDBatterySwitch openSwitch closed

    Instruction for the animatorText to be displayed in the working area (DT) If electronic logic radio button is selected, the process should follow the steps shown from slide 19 - 27 Initially show the figure in step 10 Input is given only in the toggle switch. Depending upon the input given, the switch position must change. The movement of switch must be smoothThe text in DT should appear in parallel to the figure Performing XOR logic using electronic switches Switch open represents input 0 Switch close represents input 1 LED off represents 0 LED on represents 1

    Input AInput BOutput

  • 15324

    Step 11: 10Legend:Input AInput BOutput00Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT) Then highlight small grey squares in the switch and display 0 and 0 near the horizontal lines of the gate Also show 0 and 0 in the truth table as shown The black lines at switch A and switch B should move to meet 0 and 0 The red circles in the switches represent supply from batteryThe text in DT should appear in parallel to the figureSwitch A is at 0 representing input A as 0Switch B is at 0 representing input B as 0

    Input AInput BOutput00

  • 15324

    Step 12: 10Legend:Input AInput BOutput000Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT) Show LED in OFF state Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs switch A is at 0 and switch B is at 0, there is no continuous path.Therefore there is no supply of power for LED to glowSo the LED is OFF representing 0

    Input AInput BOutput000

  • 15324

    Step 13: Input AInput BOutput10Legend:01Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight grey square in the switch at input A and red square at input BDisplay inputs as 0 and 1 near the gate as shownAlso show 0 and 1 in the truth table as shown and keep filling the truth table along with old values The black line at switch A should be moved to 0 and the line at switch B should be moved to 1The text in DT should appear in parallel to the figureSwitch A is at 0 representing input A as 0Switch B is at 1 representing input B as 1

    Input AInput BOutput00001

  • 15324

    Step 14: Input AInput BOutput10Legend:101Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT) Show LED glowing that represents LED in ON state Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs switch A is at 0 and switch B is at 1, there is a continuous path for the current to flow thereby supplying power for LED to glowSo the LED is ON representing 1

    Input AInput BOutput000011

  • 15324

    Step 15: Input AInput BOutput1010Legend:Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight red square in the switch at input A and grey square at input BDisplay inputs as 1 and 0 near the gate as shownAlso show 1 and 0 in the truth table as shown and keep filling the truth table along with old values The black line at switch A should be moved to 1 and the line at switch B should be moved to 0The text in DT should appear in parallel to the figureSwitch A is at 1 representing input A as 1Switch B is at 0 representing input B as 0

    Input AInput BOutput00001110

  • 15324

    Step 16: Input AInput BOutput11010Legend:Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT) Show LED glowing that represents LED in ON state Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs switch A is at1 and switch B is at 0, there is a continuous path for the current to flow thereby supplying power for LED to glowSo the LED is ON representing 1

    Input AInput BOutput000011101

  • 15324

    Step 17: Input AInput BOutput1110Legend:Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight red square in the switch at input A and red square at input BDisplay inputs as 1 and 1 near the gate as shownAlso show 1 and 1 in the truth table as shown and keep filling the truth table along with old values The black lines at switch A and switch B should move to meet 1 and 1The text in DT should appear in parallel to the figureSwitch A is at 1 representing input A as 1Switch B is at 1 representing input B as 1

    Input AInput BOutput00001110111

  • 15324

    Step 18: Input AInput BOutput01110Legend:Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT) Show LED in OFF state Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs switch A is at 1 and switch B is at 1, there is no continuous path.Therefore there is no supply of power for LED to glowSo the LED is OFF representing 0

    Select any radio button to view different ways of implementing XOR gate

    Input AInput BOutput000011101110

  • 15324

    XOR - ApplicationStep 19: Input AInput BOutput10Legend:When the power supply is ON,Tea button : 0 - OFF, 1- ONCoffee button: 0- OFF, 1- ONCup: 0- Empty, 1- FullRefer slide 29(next slide) for figure

    Instruction for the animatorText to be displayed in the working area (DT) If application of XOR radio button is selected, the process should follow the steps shown from slide 28 41 Initially show the figure in step 19 Input is given only in the toggle switch. Depending upon the input given, the respective button must be highlighted.(refer next slide for details) Show the switch on the switch board is ON* You can change the shape or model of power adaptor, vending machine. This image is given for reference to understand how the figure should look like in the LOThe text in DT should appear in parallel to the figureImplementation of XOR logic using vending machine Tea button OFF represents input 0 Tea button ON represents input 1Coffee button OFF represents 0 Coffee button ON represents 1 Empty cup represents 0Filled cup represents 1

    Input AInput BOutputTea buttonCoffee buttonCup

  • Tea buttonCoffee buttonPower adaptorSwitch is ON Switch boardEmpty cupPower button (it should be ON always)When A-0 and B-0 are selected, no buttons are selected and no coffee/ tea in the cup A-0 and B-1 are selected, highlight coffee(orange) button or show a hand pressing coffee button and the cup is filled with coffee(show the flow also) A-1 and B-0 are selected, highlight tea(green) button or show a hand pressing tea button and the cup is filled with tea(show the flow also) A-1 and B-1 are selected, highlight both buttons or show a hand pressing both buttons but no coffee/tea in the cup

  • 15324

    Step 20: 10Legend:Input AInput BOutput00Refer slide 31(next slide) for figure

    Instruction for the animatorText to be displayed in the working area (DT) Then highlight small grey squares in the switch and display 0 and 0 near the horizontal lines of the gate Also show 0 and 0 in the truth table as shown Show that no button on the vending machine is pressed The text in DT should appear in parallel to the figureTea button OFF represents input A as 0Coffee button OFF represents input B as 0

    Input AInput BOutputTea buttonCoffee buttonCupOFF (0)OFF (0)

  • 15324

    Step 21: 10Legend:Input AInput BOutput000Refer slide 31(previous slide) for figure

    Instruction for the animatorText to be displayed in the working area (DT) The cup should be shown empty Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs no button is pressed on the machine, no liquid comes out and the cup is emptySo the empty cup represents 0

    Input AInput BOutputTea buttonCoffee buttonCupOFF (0)OFF (0)Empty (0)

  • 15324

    Step 22: Input AInput BOutput0110Legend:Refer slide 34(next slide) for figure

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight grey square in the switch at input A and red square at input BDisplay inputs as 0 and 1 near the gate as shownAlso show 0 and 1 in the truth table as shown and keep filling the truth table along with old valuesShow that coffee button is pressed (if you can, show a hand pressing the button)The text in DT should appear in parallel to the figureTea button is OFF representing input A as 0Coffee button is pressed representing input B as 1

    Input AInput BOutputTea buttonCoffee buttonCupOFF (0)OFF (0)Empty (0)OFF (0)ON (1)

  • 15324

    Step 23: Input AInput BOutput10110Legend:Refer slide 34(previous slide) for figure

    Instruction for the animatorText to be displayed in the working area (DT) Show that cup is filled with coffee (show coffee falling into the cup) Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs coffee button is pressed on the machine, the cup is filled up with coffeeSo the filled cup represents 1

    Input AInput BOutputTea buttonCoffee buttonCupOFF (0)OFF (0)Empty (0)OFF (0)ON (1)FULL (1)

  • 15324

    Step 24: Input AInput BOutput1010Legend:Refer slide 37(next slide) for figure

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight red square in the switch at input A and grey square at input BDisplay inputs as 1 and 0 near the gate as shownAlso show 1 and 0 in the truth table as shown and keep filling the truth table along with old values Show that tea button is pressed (if you can, show a hand pressing the button)The text in DT should appear in parallel to the figureTea button is pressed representing input A as 1Coffee button is OFF representing input B as 0

    Input AInput BOutputTea buttonCoffee buttonCupOFF (0)OFF (0)Empty (0)OFF (0)ON (1)FULL (1)ON (1)OFF (0)

  • 15324

    Step 25: Input AInput BOutput10110Legend:Refer slide 37(previous slide) for figure

    Instruction for the animatorText to be displayed in the working area (DT) Show that cup is filled with tea (show tea falling into the cup) Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs tea button is pressed on the machine, the cup is filled up with teaSo the filled cup represents 1

    Input AInput BOutputTea buttonCoffee buttonCupOFF (0)OFF (0)Empty (0)OFF (0)ON (1)FULL (1)ON (1)OFF (0)FULL (1)

  • 15324

    Step 26: Input AInput BOutput1110Legend:Refer slide 40(next slide) for figure

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight red square in the switch at input A and red square at input BDisplay inputs as 1 and 1 near the gate as shownAlso show 1 and 1 in the truth table as shown and keep filling the truth table along with old values Show that both buttons on the vending machine are pressed The text in DT should appear in parallel to the figureTea button ON represents input A as 1Coffee button ON represents input B as 1

    Input AInput BOutputTea buttonCoffee buttonCupOFF (0)OFF (0)Empty (0)OFF (0)ON (1)FULL (1)ON (1)OFF (0)FULL (1)ON (1)ON (1)

  • 15324

    Step 27: Input AInput BOutput11010Legend:Refer slide 40(previous slide) for figure

    Instruction for the animatorText to be displayed in the working area (DT) The cup should be shown empty Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs both buttons are pressed on the machine, no liquid comes out and the cup is emptyThis is because an invalid signal is sent to the machineSo the empty cup represents 0

    Thus using a vending machine, XOR logic is explained

    Input AInput BOutputTea buttonCoffee buttonCupOFF (0)OFF (0)Empty (0)OFF (0)ON (1)FULL (1)ON (1)OFF (0)FULL (1)ON (1)ON (1)Empty (0)

  • 15324

    Implementation of Ex-OR using NANDStep 28: Expression Set - 1Expression Set - 2Expression Set - 3InputsOutputEquation - 1

    Instruction for the animatorText to be displayed in the working area (DT) Initially show figure in step 28The order of steps (20 steps) should follow the sequence given in table. Also see slides (44 55) for more detailsThere must be delay between each step (for delay refer table in next slide)All the minimizations should appear below the figure When showing minimization of expressions given in next slide, all the steps should come one after the other. (with a delay of 1 second between steps)The text in DT should appear in parallel to the figure Implementation of XOR using NAND Inputs A and BOutput X For the minimization rules, refer Boolean algebra and De Morgans Theorems

    Thus using NAND, XOR logic is implemented

  • Steps (4 20): refer slides (44 55)

    Sr. NoSequence of steps to be displayedDelay between each step1Figure in black-2Text InputsAfter 2 seconds3A and B in redAfter 2 seconds4Color change of input lines After 2 seconds5Color change of output lineAfter 2 seconds6Equation 1 After 2 seconds7Color change of input lines After 2 seconds8Color change of output lineAfter 2 seconds9Expression set 1 Show at a time 10Minimization of expression set 1 11Color change of input lines 12Color change of output line13Expression set 2 14Minimization of expression set 2 15Color change of input lines 16Color change of output line17Text Output18X in red19Expression set 320Minimization of expression set 3

  • Expression Set - 1Expression Set - 1Expression Set - 1Expression Set - 1In expression set -1, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • Expression Set - 2Expression Set - 2In expression set -2, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • Expression Set - 3Expression Set - 3In expression set -3, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • 15324

    Implementation of Ex-OR using NORStep 29: Expression Set - 1Expression Set - 2InputsOutputEquation - 1Equation - 2Equation - 3

    Instruction for the animatorText to be displayed in the working area (DT) Initially show figure in step 29The order of steps (22 steps) should follow the sequence given in table. Also see slides (58 72) for more detailsThere must be delay between each step (for delay refer table in next slide)All the minimizations should appear below the figureWhen showing minimization of expressions given in next slide, all the steps should come one after the other. (with a delay of 1 second between steps)The text in DT should appear in parallel to the figure Implementation of XOR using NOR Inputs A and BOutput X For the minimization rules, refer Boolean algebra and De Morgans Theorems

    Thus using NOR, XOR logic is implemented

  • Steps (4 22): refer slides (58 72)

    Sr. NoSequence of steps to be displayedDelay between each step1Figure in black-2Text InputsAfter 2 seconds3A and B in redAfter 2 seconds4Color change of input lines After 2 seconds5Color change of output lineAfter 2 seconds6Equation 1 After 2 seconds7Color change of input lines After 2 seconds8Color change of output lineAfter 2 seconds9Equation 2 After 2 seconds10Color change of input lines After 2 seconds11Color change of output lineAfter 2 seconds12Equation 3 After 2 seconds13Color change of input lines After 2 seconds14Color change of output lineAfter 2 seconds15Expression set 1Show at a time

    16Minimization of expression set 117Color change of input lines 18Color change of output line19Text Output20X in red21Expression set 222Minimization of expression set 2

  • Expression Set - 1Expression Set - 1In expression set -1, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • Expression Set - 2Expression Set - 2In expression set -2, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • Step 1: 15324

    XNORInput AInput BOutput10Legend:Truth Table:1 - input is HIGH 0- input is LOW

    Instruction for the animatorText to be displayed in the working area (DT) Initially only Gate menu is enabled and all other buttons are disabled (check slide 125 for more details)When user selects any Gate from Gate Menu, Show the respective gate symbol and display as it is shown in master layout fig. A Once the gate is selected, enable/highlight four radio buttons basic concept of the gate, electronic logic, implementation of XNOR using NAND, implementation of XNOR using NORFollow the steps as shown in stepwise process. If basic concept of the GATE radio button is selected, the process should follow the steps shown from slide 73 81 If electronic logic is selected, the process should follow the steps shown from slide 82 90 If implementation of XNOR using NAND is selected, the process should follow the steps shown from slide 91 110 If implementation of XNOR using NOR is selected, the process should follow the steps shown from slide 111 124 The text in DT should appear in parallel to the figuresSelect Gate from Gate menu

    The 2-input XNOR gate symbol and its truth table. 1 represents input HIGH 0 represents input LOW

    Input AInput BOutput

  • Step 2: 15324

    Basic concept of the XNOR gateInput AInput BOutput0010Legend:

    Instruction for the animatorText to be displayed in the working area (DT) If basic concept of gate radio button is selected, the process should follow the steps shown from slide 73 81 Initially show the figure in step 1, then highlight small grey squares in the switch and display 0 and 0 near the horizontal lines of the gate as shown Also show 0 and 0 in the truth table Then display 0 . 0 inside the gate The text in DT should appear in parallel to the figureInput A is 0 Input B is 0

    Input AInput BOutput00

  • Step 3: 15324

    Input AInput BOutput10010Legend:

    Instruction for the animatorText to be displayed in the working area (DT) Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureThe output is 1

    Input AInput BOutput001

  • Step 4: 15324

    Input AInput BOutput10Legend:01

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight grey square in the switch at input A and red square at input BDisplay inputs as 0 and 1 near the gate as shownAlso show 0 and 1 in the truth table as shown and keep filling the truth table along with old valuesThen display 0 . 1 inside the gate The text in DT should appear in parallel to the figureInput A is 0 Input B is 1

    Input AInput BOutput00101

  • Step 5: 15324

    Input AInput BOutput10Legend:001

    Instruction for the animatorText to be displayed in the working area (DT) Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureThe output is 0

    Input AInput BOutput001010

  • Step 6: 15324

    10Legend:Input AInput BOutput10

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight red square in the switch at input A and grey square at input BDisplay inputs as 1 and 0 near the gate as shownAlso show 1 and 0 in the truth table as shown and keep filling the truth table along with old valuesThen display 1 . 0 inside the gate The text in DT should appear in parallel to the figureInput A is 1 Input B is 0

    Input AInput BOutput00101010

  • Step 7: 15324

    10Legend:Input AInput BOutput010

    Instruction for the animatorText to be displayed in the working area (DT) Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureThe output is 0

    Input AInput BOutput001010100

  • Step 8: 15324

    10Legend:Input AInput BOutput11

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight red square in the switch at input A and red square at input BDisplay inputs as 1 and 1 near the gate as shownAlso show 1 and 1 in the truth table as shown and keep filling the truth table along with old valuesThen display 1 . 1 inside the gate The text in DT should appear in parallel to the figureInput A is 1Input B is 1

    Input AInput BOutput00101010011

  • Step 9: 15324

    10Legend:Input AInput BOutput111

    Instruction for the animatorText to be displayed in the working area (DT) Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureThe output is 1

    Select any radio button to view different ways of implementing XNOR gate

    Input AInput BOutput001010100111

  • Step 10: 15324

    XNOR gate using Switches10Legend:Input AInput BOutputUsing Electronic switchesLEDBatterySwitch openSwitch closed

    Instruction for the animatorText to be displayed in the working area (DT) If electronic logic radio button is selected, the process should follow the steps shown from slide 82 90 Initially show the figure in step 10 Input is given only in the toggle switch. Depending upon the input given, the switch position must change. The movement of switch must be smoothThe text in DT should appear in parallel to the figure Performing XNOR logic using electronic switches Switch open represents input 0 Switch close represents input 1 LED off represents 0 LED on represents 1

    Input AInput BOutput

  • 15324

    Step 11: 10Legend:Input AInput BOutput00Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT) Then highlight small grey squares in the switch and display 0 and 0 near the horizontal lines of the gate Also show 0 and 0 in the truth table as shown The black lines at switch A and switch B should be moved up to meet 0 and 0The text in DT should appear in parallel to the figureSwitch A is at 0 representing input A as 0Switch B is at 0 representing input B as 0

    Input AInput BOutput00

  • 15324

    Step 12: 10Legend:Input AInput BOutput001Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT) Show LED glowing that represents LED in ON state Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs both the switches are at 0, there is a continuous path for the current to flow thereby supplying power for LED to glowSo the LED is ON representing 1

    Input AInput BOutput001

  • 15324

    Step 13: Input AInput BOutput10Legend:01Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight grey square in the switch at input A and red square at input BDisplay inputs as 0 and 1 near the gate as shownAlso show 0 and 1 in the truth table as shown and keep filling the truth table along with old values The black line at switch A should be moved to 0 and the line at switch B should be moved to 1The text in DT should appear in parallel to the figureSwitch A is at 0 representing input A as 0Switch B is at 1 representing input B as 1

    Input AInput BOutput00101

  • 15324

    Step 14: Input AInput BOutput10Legend:001Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT) Show LED in OFF state Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs switch A is at 0 and switch B is at 1, there is no continuous path.Therefore there is no supply of power for LED to glowSo the LED is OFF representing 0

    Input AInput BOutput001010

  • 15324

    Step 15: Input AInput BOutput1010Legend:Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight red square in the switch at input A and grey square at input BDisplay inputs as 1 and 0 near the gate as shownAlso show 1 and 0 in the truth table as shown and keep filling the truth table along with old values The black line at switch A should be moved to 1 and the line at switch B should be moved to 0The text in DT should appear in parallel to the figureSwitch A is at 1 representing input A as 1Switch B is at 0 representing input B as 0

    Input AInput BOutput00101010

  • 15324

    Step 16: Input AInput BOutput01010Legend:Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT) Show LED in OFF state Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs switch A is at 1 and switch B is at 0, there is no continuous path.Therefore there is no supply of power for LED to glowSo the LED is OFF representing 0

    Input AInput BOutput001010100

  • 15324

    Step 17: Input AInput BOutput1110Legend:Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT)Then highlight red square in the switch at input A and red square at input BDisplay inputs as 1 and 1 near the gate as shownAlso show 1 and 1 in the truth table as shown and keep filling the truth table along with old values The black lines at switch A and switch B should be moved down to meet 1 and 1The text in DT should appear in parallel to the figureSwitch A is at 1 representing input A as 1Switch B is at 1 representing input B as 1

    Input AInput BOutput00101010011

  • 15324

    Step 18: Input AInput BOutput11110Legend:Using Electronic switches

    Instruction for the animatorText to be displayed in the working area (DT) Show LED glowing that represents LED in ON state Then show the output in the given square box. Change the color of the box and output as wellThe text in DT should appear in parallel to the figureAs both the switches are at 1, there is a continuous path for the current to flow thereby supplying power for LED to glowSo the LED is ON representing 1

    Select any radio button to view different ways of implementing XNOR gate

    Input AInput BOutput001010100111

  • 15324

    Implementation of Ex-NOR using NANDStep 19: Refer slide 92(next slide) for figure

    Instruction for the animatorText to be displayed in the working area (DT) Initially show figure in step 19The order of steps (24 steps) should follow the sequence given in table. Also see slides (95 110) for more detailsThere must be delay between each step (for delay refer table in next slide)All the minimizations should appear below the figureWhen showing minimization of expressions given in next slide, all the steps should come one after the other. (with a delay of 1 second between steps)The text in DT should appear in parallel to the figure Implementation of XNOR using NAND Inputs A and BOutput X For the minimization rules, refer Boolean algebra and De Morgans Theorems

    Thus using NAND, XNOR logic is implemented

  • Expression Set - 1Expression Set - 2Expression Set - 3Expression Set - 4InputsOutputEquation- 1

  • Steps (4 24): refer slides (95 110)

    Sr. NoSequence of steps to be displayedDelay between each step1Figure in black-2Text InputsAfter 2 seconds3A and B in redAfter 2 seconds4Color change of input lines After 2 seconds5Color change of output lineAfter 2 seconds6Equation 1 After 2 seconds7Color change of input lines After 2 seconds8Color change of output lineAfter 2 seconds9Expression set 1 Show at a time 10Minimization of expression set 1 11Color change of input lines 12Color change of output line13Expression set 2 14Minimization of expression set 2 15Color change of input lines 16Color change of output line17Expression set 318Minimization of expression set 3

  • Steps (4 24): refer slides (95 110)

    Sr. NoSequence of steps to be displayedDelay between each step19Color change of input lines After 2 seconds20Color change of output lineAfter 2 seconds21Text OutputAfter 2 seconds22X in redAfter 2 seconds23Expression set 3Show at a time 24Minimization of expression set 3

  • Expression Set - 1Expression Set - 1In expression set -1, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • Expression Set - 2Expression Set - 2In expression set -2, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • Expression Set - 3Expression Set - 3In expression set -3, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • Refer next slide for expression set - 4Expression Set - 4

  • Minimization of expressions for the animation (XNOR using NAND):Expression Set - 4In expression set -4, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • 15324

    Implementation of Ex-NOR using NORStep 20: Expression Set - 1Expression Set - 2Expression Set - 3InputsOutputEquation- 1

    Instruction for the animatorText to be displayed in the working area (DT) Initially show figure in step 20The order of steps (20 steps) should follow the sequence given in table. Also see slides (113 124 ) for more detailsThere must be delay between each step (for delay refer table in next slide)All the minimizations should appear below the figureWhen showing minimization of expressions given in next slide, all the steps should come one after the other. (with a delay of 1 second between steps)The text in DT should appear in parallel to the figure Implementation of XNOR using NOR Inputs A and BOutput X For the minimization rules, refer Boolean algebra and De Morgans Theorems

    Thus using NOR, XNOR logic is implemented

  • Steps (4 24): refer slides (95 72)

    Sr. NoSequence of steps to be displayedDelay between each step1Figure in black-2Text InputsAfter 2 seconds3A and B in redAfter 2 seconds4Color change of input lines After 2 seconds5Color change of output lineAfter 2 seconds6Equation 1 After 2 seconds7Color change of input lines After 2 seconds8Color change of output lineAfter 2 seconds9Expression set 1 Show at a time 10Minimization of expression set 1 11Color change of input lines 12Color change of output line13Expression set 2 14Minimization of expression set 2 15Color change of input lines 16Color change of output line17Text Output18X in red19Expression set 320Minimization of expression set 3

  • Expression Set - 1Expression Set - 1In expression set -1, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • Expression Set - 2Expression Set - 2In expression set -2, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • Expression Set - 3Expression Set - 3In expression set -3, first display only left hand side of = (equal to) in the figure. Then minimization has to be shown After minimization is done then show the right hand side expression in the figure

  • IntroductionCredits*DefinitionsTest your understanding (questionnaire)Lets Sum up (summary)Want to know more(Further Reading)Try it yourselfInteractivity:AnalogySlide 1Slide 3Slide 125 129 Slide 130Electrical EngineeringThe demo itself is interactivity in this LO Initially only Gate menu must be enabled, all other buttons should be disabled Text Select any gate from Gate Menu is to be displayed in DT area When user selects any Gate from Gate Menu, Show the respective gate symbol, empty truth table as shown in master layout fig. A After gate is selected, then enable respective radio buttons Also display the text in DT area Select any radio button to view different ways of implementing ____ logic (the blank is to be filled depending upon the respective gate selected) After any one radio button is selected, enable START button After START is pressed, enable PAUSE, Auto-run, Stepper, RESET/STOP buttons Display the text Press Auto-run or Stepper buttons to view the animation Then display the text Click on red or grey buttons of toggle switch to give input Input if user clicks red, input should be displayed as 1 if user clicks grey, input should be displayed as 0

    10Legend: Toggle switch

  • QuestionnaireWhich of the figures (a to d) is equivalent to figure A

    Answers: a) c)

    b) d)

    15243Fig. A***Answers are given in red

  • Questionnaire2. What is X (output waveform) if A and B (input waveforms) are given as shown in figure?

    Answers: a) b) c)

    d) 15243

  • Questionnaire

    3. Which of the figures (a to d) is the De Morgans equivalent of figure A?

    Answers: a) b)

    c) d)15243Fig. A

  • Questionnaire

    4. Consider a staircase having an overhead light. There are two toggle switches A and B (one each on one level of the staircase) to turn the light ON and OFF. (See fig. A) next slide Initially both the switches are in 0 state i.e., OFF. The light is switched ON using switch B but it is switched OFF using switch A. Which logic gate can be used to implement the above logic?

    Hint: Compute truth table of the logic gate assuming switches A and B as its inputs and light as its output

    Answers: a) NANDb) NORc) XNORd) XOR15243

  • Fig. A

  • Questionnaire

    5. Which of the following are TRUE about XNOR?It produces a LOW output when its inputs are same It produces a HIGH output when its inputs are same It is also referred to as Equivalence gate Output of XNOR is same as the inverted output of XOR

    Answers: a) I, III,IVb) II, III, IVc) III,IVd) Only I15243

  • Links for further readingReference websites:http://en.wikipedia.org/wiki/Logic_gatehttp://www.wisc-online.com/Objects/ViewObject.aspx?ID=dig1302 http://www.mekanizmalar.com/logic_gates.html http://www.williamson-labs.com/480_logic.htmhttp://isweb.redwoods.cc.ca.us/instruct/calderwoodd/diglogic/http://www.w3professors.com/Pages/Courses/DCLD/Digital-Circuits-and-Logic-Designs.html http://homepages.inf.ed.ac.uk/rbf/HIPR2/arthops.htmBooks:Digital Systems: Principles and Applications by Ronald-J.-Tocci

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