Logic Gates Part – III : Combinational Logic Gates Combinational Logic Circuits are made up from basic logic NAND, NOR or NOT gates that are "combined"

Logic Gates Part – 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 Chitta  Mentor: Aruna Adil, Prof. C. Amarnath *The contents in this ppt are licensed under Creative Commons Attribution-NonCommercial-ShareAlike 2.5 India license

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

Definitions of the components/Keywords: 5 3 2 4 1 1. LOGIC: Reasoning conducted or assessed according to strict principles of validity. 2.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. 3.INPUT: The signal which is given to get the desired output 4.OUTPUT: Anything that comes out 5.XOR GATE:The output is high (1) if its inputs are at opposite states. 6.XNOR GATE: :The output is high (1) if its inputs are at same states. 7.TRUTH TABLE : A truth table is a table that shows all the input-output possibilities of a logic circuit. 8.LOGICAL EXPRESSION: A logical expression consists of one or more logical operators and logical, numeric, or relational operands. 9.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: 5 3 2 4 1 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 1 Definitions of the components/Keywords: 5 3 2 4 1

5 3 2 4 1 Symbols 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 B B A X = A B = A + B = A B + A B B A X = A + B = A B + A B Input Output A+B = A∙B A∙B = A+B 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.

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: 5 3 2 4 1 B A X = A + B Input 1Input 2Output AB 000 011 101 110

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: 5 3 2 4 1 B A X = A B = A + B Input 1Input 2Output AB 001 010 100 111

Master Layout 5 3 2 4 1 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 pressed Give a text area to display the status of the simulation Fig. A Simulation 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 A Input B Output GATE Symbol Truth Table: Control Area 1010 Legend: Toggle Switch ‘1’ - 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: 1 5 3 2 4 XOR Instruction for the animator Text 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 NOR Follow 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 figures Select 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 Input A Input B Output 1010 Legend: Truth Table: ‘1’ - input is HIGH ‘0’- input is LOW

Step 2: 1 5 3 2 4 Basic concept of the XOR gate I nstruction for the animator T ext 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 - 18 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 figure Input A is 0 Input B is 0 Input AInput BOutput 00 Input A Input B Output 0 0 1010 Legend:

Step 3: 1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure The output is 0 Input AInput BOutput 000 Input A Input B Output 0 0 0 1010 Legend:

Step 4: 1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight grey square in the switch at input A and red square at input B Display inputs as 0 and 1 near the gate as shown Also show 0 and 1 in the truth table as shown and keep filling the truth table along with old values Then display 0 + 1 inside the gate The text in DT should appear in parallel to the figure Input A is 0 Input B is 1 Input AInput BOutput 000 01 Input A Input B Output 1010 Legend: 0 1

Step 5: 1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure The output is 1 Input AInput BOutput 000 011 Input A Input B Output 1010 Legend: 1 0 1

Step 6: 1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight red square in the switch at input A and grey square at input B Display inputs as 1 and 0 near the gate as shown Also show 1 and 0 in the truth table as shown and keep filling the truth table along with old values Then display 1 + 0 inside the gate The text in DT should appear in parallel to the figure Input A is 1 Input B is 0 1010 Legend: Input AInput BOutput 000 011 10 Input A Input B Output 1 0

Step 7: 1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure The output is 1 1010 Legend: Input AInput BOutput 000 011 101 Input A Input B Output 1 1 0

Step 8: 1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight red square in the switch at input A and red square at input B Display inputs as 1 and 1 near the gate as shown Also show 1 and 1 in the truth table as shown and keep filling the truth table along with old values Then display 1 + 1 inside the gate The text in DT should appear in parallel to the figure Input A is 1 Input B is 1 1010 Legend: Input AInput BOutput 000 011 101 11 Input A Input B Output 1 1

Step 9: 1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure The output is 0 Select any radio button to view different ways of implementing XOR 1010 Legend: Input AInput BOutput 000 011 101 110 Input A Input B Output 0 1 1

Step 10: 1 5 3 2 4 XOR gate using Switches I nstruction for the animator T ext 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 smooth The 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 1010 Legend: Input AInput BOutput Input A Input B Output Using Electronic switches LED Battery Switch open Switch closed

1 5 3 2 4 I nstruction for the animator T ext 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 battery The text in DT should appear in parallel to the figure Switch A is at 0 representing input A as 0 Switch B is at 0 representing input B as 0 Step 11: 1010 Legend: Input AInput BOutput 00 Input A Input B Output 0 0 Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As 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 glow So the LED is OFF representing 0 Step 12: 1010 Legend: Input AInput BOutput 000 Input A Input B Output 0 0 0 Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight grey square in the switch at input A and red square at input B Display inputs as 0 and 1 near the gate as shown Also 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 1 The text in DT should appear in parallel to the figure Switch A is at 0 representing input A as 0 Switch B is at 1 representing input B as 1 Step 13: Input AInput BOutput 000 01 Input A Input B Output 1010 Legend: 0 1 Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As 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 glow So the LED is ON representing 1 Step 14: Input AInput BOutput 000 011 Input A Input B Output 1010 Legend: 1 0 1 Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight red square in the switch at input A and grey square at input B Display inputs as 1 and 0 near the gate as shown Also 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 0 The text in DT should appear in parallel to the figure Switch A is at 1 representing input A as 1 Switch B is at 0 representing input B as 0 Step 15: Input AInput BOutput 000 011 10 Input A Input B Output 1 0 1010 Legend: Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As 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 glow So the LED is ON representing 1 Step 16: Input AInput BOutput 000 011 101 Input A Input B Output 1 1 0 1010 Legend: Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight red square in the switch at input A and red square at input B Display inputs as 1 and 1 near the gate as shown Also 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 1 The text in DT should appear in parallel to the figure Switch A is at 1 representing input A as 1 Switch B is at 1 representing input B as 1 Step 17: Input AInput BOutput 000 011 101 11 Input A Input B Output 1 1 1010 Legend: Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As 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 glow So the LED is OFF representing 0 Select any radio button to view different ways of implementing XOR gate Step 18: Input AInput BOutput 000 011 101 110 Input A Input B Output 0 1 1 1010 Legend: Using Electronic switches

1 5 3 2 4 XOR - Application I nstruction for the animator T ext 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 LO The text in DT should appear in parallel to the figure Implementation of XOR logic using vending machine Tea button OFF represents input 0 Tea button ON represents input 1 Coffee button OFF represents 0 Coffee button ON represents 1 Empty cup represents 0 Filled cup represents 1 Step 19: Input A Input B Output 1010 Legend: Input AInput BOutput Tea button Coffee button Cup When the power supply is ON, Tea button : 0 - OFF, 1- ON Coffee button: 0- OFF, 1- ON Cup: 0- Empty, 1- Full Refer slide 29(next slide) for figure

Tea button Coffee button Power adaptor Switch is ON Switch board Empty cup Power 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

1 5 3 2 4 I nstruction for the animator T ext 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 figure Tea button OFF represents input A as 0 Coffee button OFF represents input B as 0 Step 20: 1010 Legend: Input A Input B Output 0 0 Input AInput BOutput Tea button Coffee button Cup OFF (0) Refer slide 31(next slide) for figure

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As no button is pressed on the machine, no liquid comes out and the cup is empty So the empty cup represents 0 Step 21: 1010 Legend: Input A Input B Output 0 0 0 Input AInput BOutput Tea button Coffee button Cup OFF (0) Empty (0) Refer slide 31(previous slide) for figure

1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight grey square in the switch at input A and red square at input B Display inputs as 0 and 1 near the gate as shown Also show 0 and 1 in the truth table as shown and keep filling the truth table along with old values Show that coffee button is pressed (if you can, show a hand pressing the button) The text in DT should appear in parallel to the figure Tea button is OFF representing input A as 0 Coffee button is pressed representing input B as 1 Step 22: Input A Input B Output 0 1 1010 Legend: Input AInput BOutput Tea button Coffee button Cup OFF (0) Empty (0) OFF (0)ON (1) Refer slide 34(next slide) for figure

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As coffee button is pressed on the machine, the cup is filled up with coffee So the filled cup represents 1 Step 23: Input A Input B Output 1 0 1 1010 Legend: Input AInput BOutput Tea button Coffee button Cup OFF (0) Empty (0) OFF (0)ON (1)FULL (1) Refer slide 34(previous slide) for figure

1 5 3 2 4 Step 24: Input A Input B Output 1 0 1010 Legend: I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight red square in the switch at input A and grey square at input B Display inputs as 1 and 0 near the gate as shown Also 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 figure Tea button is pressed representing input A as 1 Coffee button is OFF representing input B as 0 Input AInput BOutput Tea button Coffee button Cup OFF (0) Empty (0) OFF (0)ON (1)FULL (1) ON (1)OFF (0) Refer slide 37(next slide) for figure

1 5 3 2 4 Step 25: Input A Input B Output 1 0 1 1010 Legend: I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As tea button is pressed on the machine, the cup is filled up with tea So the filled cup represents 1 Input AInput BOutput Tea button Coffee button Cup OFF (0) Empty (0) OFF (0)ON (1)FULL (1) ON (1)OFF (0)FULL (1) Refer slide 37(previous slide) for figure

1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight red square in the switch at input A and red square at input B Display inputs as 1 and 1 near the gate as shown Also 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 figure Tea button ON represents input A as 1 Coffee button ON represents input B as 1 Step 26: Input A Input B Output 1 1 1010 Legend: Input AInput BOutput Tea button Coffee button Cup OFF (0) Empty (0) OFF (0)ON (1)FULL (1) ON (1)OFF (0)FULL (1) ON (1) Refer slide 40(next slide) for figure

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As both buttons are pressed on the machine, no liquid comes out and the cup is empty This is because an invalid signal is sent to the machine So the empty cup represents 0 Thus using a vending machine, XOR logic is explained Step 27: Input A Input B Output 1 1 0 1010 Legend: Input AInput BOutput Tea button Coffee button Cup OFF (0) Empty (0) OFF (0)ON (1)FULL (1) ON (1)OFF (0)FULL (1) ON (1) Empty (0) Refer slide 40(previous slide) for figure

1 5 3 2 4 Implementation of Ex-OR using NAND I nstruction for the animator T ext to be displayed in the working area (DT) Initially show figure in step 28 The order of steps (20 steps) should follow the sequence given in table. Also see slides (44 – 55) for more details There 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 B Output X For the minimization rules, refer Boolean algebra and De Morgan’s Theorems Thus using NAND, XOR logic is implemented Step 28: Expression Set - 1 Expression Set - 2 Expression Set - 3 Inputs Output Equation - 1

Sr. NoSequence of steps to be displayedDelay between each step 1Figure in black- 2Text ‘Inputs’After 2 seconds 3A and B in redAfter 2 seconds 4Color change of input linesAfter 2 seconds 5Color change of output lineAfter 2 seconds 6Equation – 1After 2 seconds 7Color change of input linesAfter 2 seconds 8Color change of output lineAfter 2 seconds 9Expression set – 1Show at a time 10Minimization of expression set – 1 11Color change of input lines 12Color change of output line 13Expression set – 2 14Minimization of expression set – 2 15Color change of input lines 16Color change of output line 17Text ‘Output’ 18‘X’ in red 19Expression set – 3 20Minimization of expression set – 3 Steps (4 – 20): refer slides (44 – 55)

Expression Set - 1 In 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

1 5 3 2 4 Implementation of Ex-OR using NOR Step 29: Expression Set - 1 Expression Set - 2 Inputs Output I nstruction for the animator T ext to be displayed in the working area (DT) Initially show figure in step 29 The order of steps (22 steps) should follow the sequence given in table. Also see slides (58 – 72) for more details There 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 NOR Inputs A and B Output X For the minimization rules, refer Boolean algebra and De Morgan’s Theorems Thus using NOR, XOR logic is implemented Equation - 1 Equation - 2 Equation - 3

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

Step 1: 1 5 3 2 4 XNOR Instruction for the animator Text 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 NOR Follow 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 figures Select 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 Input A Input B Output 1010 Legend: Truth Table: ‘1’ - input is HIGH ‘0’- input is LOW

Step 2: 1 5 3 2 4 Basic concept of the XNOR gate I nstruction for the animator T ext 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 figure Input A is 0 Input B is 0 Input AInput BOutput 00 Input A Input B Output 0 0 1010 Legend:

Step 3: 1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure The output is 1 Input AInput BOutput 001 Input A Input B Output 1 0 0 1010 Legend:

Step 4: 1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight grey square in the switch at input A and red square at input B Display inputs as 0 and 1 near the gate as shown Also show 0 and 1 in the truth table as shown and keep filling the truth table along with old values Then display 0. 1 inside the gate The text in DT should appear in parallel to the figure Input A is 0 Input B is 1 Input AInput BOutput 001 01 Input A Input B Output 1010 Legend: 0 1

Step 5: 1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure The output is 0 Input AInput BOutput 001 010 Input A Input B Output 1010 Legend: 0 0 1

Step 6: 1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight red square in the switch at input A and grey square at input B Display inputs as 1 and 0 near the gate as shown Also show 1 and 0 in the truth table as shown and keep filling the truth table along with old values Then display 1. 0 inside the gate The text in DT should appear in parallel to the figure Input A is 1 Input B is 0 1010 Legend: Input AInput BOutput 001 010 10 Input A Input B Output 1 0

Step 7: 1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure The output is 0 1010 Legend: Input AInput BOutput 001 010 100 Input A Input B Output 0 1 0

Step 8: 1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight red square in the switch at input A and red square at input B Display inputs as 1 and 1 near the gate as shown Also show 1 and 1 in the truth table as shown and keep filling the truth table along with old values Then display 1. 1 inside the gate The text in DT should appear in parallel to the figure Input A is 1 Input B is 1 1010 Legend: Input AInput BOutput 001 010 100 11 Input A Input B Output 1 1

Step 9: 1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure The output is 1 Select any radio button to view different ways of implementing XNOR gate 1010 Legend: Input AInput BOutput 001 010 100 111 Input A Input B Output 1 1 1

Step 10: 1 5 3 2 4 XNOR gate using Switches I nstruction for the animator T ext 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 smooth The 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 1010 Legend: Input AInput BOutput Input A Input B Output Using Electronic switches LED Battery Switch open Switch closed

1 5 3 2 4 I nstruction for the animator T ext 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 0 The text in DT should appear in parallel to the figure Switch A is at 0 representing input A as 0 Switch B is at 0 representing input B as 0 Step 11: 1010 Legend: Input AInput BOutput 00 Input A Input B Output 0 0 Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As both the switches are at 0, there is a continuous path for the current to flow thereby supplying power for LED to glow So the LED is ON representing 1 Step 12: 1010 Legend: Input AInput BOutput 001 Input A Input B Output 0 0 1 Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight grey square in the switch at input A and red square at input B Display inputs as 0 and 1 near the gate as shown Also 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 1 The text in DT should appear in parallel to the figure Switch A is at 0 representing input A as 0 Switch B is at 1 representing input B as 1 Step 13: Input AInput BOutput 001 01 Input A Input B Output 1010 Legend: 0 1 Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As 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 glow So the LED is OFF representing 0 Step 14: Input AInput BOutput 001 010 Input A Input B Output 1010 Legend: 0 0 1 Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight red square in the switch at input A and grey square at input B Display inputs as 1 and 0 near the gate as shown Also 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 0 The text in DT should appear in parallel to the figure Switch A is at 1 representing input A as 1 Switch B is at 0 representing input B as 0 Step 15: Input AInput BOutput 001 010 10 Input A Input B Output 1 0 1010 Legend: Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As 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 glow So the LED is OFF representing 0 Step 16: Input AInput BOutput 001 010 100 Input A Input B Output 0 1 0 1010 Legend: Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext to be displayed in the working area (DT) Then highlight red square in the switch at input A and red square at input B Display inputs as 1 and 1 near the gate as shown Also 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 1 The text in DT should appear in parallel to the figure Switch A is at 1 representing input A as 1 Switch B is at 1 representing input B as 1 Step 17: Input AInput BOutput 001 010 100 11 Input A Input B Output 1 1 1010 Legend: Using Electronic switches

1 5 3 2 4 I nstruction for the animator T ext 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 well The text in DT should appear in parallel to the figure As both the switches are at 1, there is a continuous path for the current to flow thereby supplying power for LED to glow So the LED is ON representing 1 Select any radio button to view different ways of implementing XNOR gate Step 18: Input AInput BOutput 001 010 100 111 Input A Input B Output 1 1 1 1010 Legend: Using Electronic switches

1 5 3 2 4 Implementation of Ex-NOR using NAND Step 19: I nstruction for the animator T ext to be displayed in the working area (DT) Initially show figure in step 19 The order of steps (24 steps) should follow the sequence given in table. Also see slides (95 – 110) for more details There 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 XNOR using NAND Inputs A and B Output X For the minimization rules, refer Boolean algebra and De Morgan’s Theorems Thus using NAND, XNOR logic is implemented Refer slide 92(next slide) for figure

Expression Set - 1 Expression Set - 2 Expression Set - 3 Expression Set - 4 Inputs Output Equation- 1

Sr. NoSequence of steps to be displayedDelay between each step 1Figure in black- 2Text ‘Inputs’After 2 seconds 3A and B in redAfter 2 seconds 4Color change of input linesAfter 2 seconds 5Color change of output lineAfter 2 seconds 6Equation – 1After 2 seconds 7Color change of input linesAfter 2 seconds 8Color change of output lineAfter 2 seconds 9Expression set – 1Show at a time 10Minimization of expression set – 1 11Color change of input lines 12Color change of output line 13Expression set – 2 14Minimization of expression set – 2 15Color change of input lines 16Color change of output line 17Expression set – 3 18Minimization of expression set – 3 Steps (4 – 24): refer slides (95 – 110)

Sr. NoSequence of steps to be displayedDelay between each step 19Color change of input linesAfter 2 seconds 20Color change of output lineAfter 2 seconds 21Text ‘Output’After 2 seconds 22‘X’ in redAfter 2 seconds 23Expression set – 3Show at a time 24Minimization of expression set – 3 Steps (4 – 24): refer slides (95 – 110)

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

Minimization of expressions for the animation (XNOR using NAND): Expression Set - 4 In 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

1 5 3 2 4 Implementation of Ex-NOR using NOR Step 20: Expression Set - 1 Expression Set - 2 Expression Set - 3 Inputs Output I nstruction for the animator T ext to be displayed in the working area (DT) Initially show figure in step 20 The order of steps (20 steps) should follow the sequence given in table. Also see slides (113 – 124 ) for more details There 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 XNOR using NOR Inputs A and B Output X For the minimization rules, refer Boolean algebra and De Morgan’s Theorems Thus using NOR, XNOR logic is implemented Equation- 1

Sr. NoSequence of steps to be displayedDelay between each step 1Figure in black- 2Text ‘Inputs’After 2 seconds 3A and B in redAfter 2 seconds 4Color change of input linesAfter 2 seconds 5Color change of output lineAfter 2 seconds 6Equation – 1After 2 seconds 7Color change of input linesAfter 2 seconds 8Color change of output lineAfter 2 seconds 9Expression set – 1Show at a time 10Minimization of expression set – 1 11Color change of input lines 12Color change of output line 13Expression set – 2 14Minimization of expression set – 2 15Color change of input lines 16Color change of output line 17Text ‘Output’ 18‘X’ in red 19Expression set – 3 20Minimization of expression set – 3 Steps (4 – 24): refer slides (95 – 72)

Introduction Credits 125 Definitions Test your understanding (questionnaire) ‏ Lets Sum up (summary) ‏ Want to know more… (Further Reading) ‏ Try it yourself Interactivity: Analogy Slide 1 Slide 3 Slide 125 – 129 Slide 130 Electrical Engineering The 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 1010 Legend: Toggle switch

Questionnaire 1.Which of the figures (a to d) is equivalent to figure A Answers: a) c) b) d) 1 5 2 4 3 Fig. A ***Answers are given in red

Questionnaire 2. What is X (output waveform) if A and B (input waveforms) are given as shown in figure? Answers: a) b) c) d) 1 5 2 4 3

Questionnaire 3. Which of the figures (a to d) is the De Morgan’s equivalent of figure A? Answers: a) b) c) d) 1 5 2 4 3 Fig. 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) NAND b) NOR c) XNOR d) XOR 1 5 2 4 3

Fig. A

Questionnaire 5. Which of the following are TRUE about XNOR? I.It produces a LOW output when its inputs are same II.It produces a HIGH output when its inputs are same III. It is also referred to as Equivalence gate IV. Output of XNOR is same as the inverted output of XOR Answers: a) I, III,IV b) II, III, IV c) III,IV d) Only I 1 5 2 4 3

Links for further reading Reference websites: http://en.wikipedia.org/wiki/Logic_gate http://www.wisc-online.com/Objects/ViewObject.aspx?ID=dig1302 http://www.mekanizmalar.com/logic_gates.html http://www.williamson-labs.com/480_logic.htm http://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.htm Books: Digital Systems: Principles and Applications by Ronald-J.-Tocci

Logic Gates Part – III : Combinational Logic Gates Combinational Logic Circuits are made up from basic logic NAND, NOR or NOT gates that are "combined"

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Logic Gates Part – III : Combinational Logic Gates Combinational Logic Circuits are made up from basic logic NAND, NOR or NOT gates that are "combined"

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Presentation on theme: "Logic Gates Part – III : Combinational Logic Gates Combinational Logic Circuits are made up from basic logic NAND, NOR or NOT gates that are "combined""— Presentation transcript:

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