Logic Gates Part – II : Universal Logic Gates

Logic Gates Part – II : Universal Logic Gates A universal gate is a gate which can implement any Boolean function without using any other gate type. NAND and NOR are the universal logic 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 universal logic gates

Definitions of the components/Keywords: 1 • 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 output • OUTPUT: Anything that comes out • NAND GATE:The output is high (1) if anyone of the inputs is low(0). • NOR GATE: :The output is low (0) if anyone of the inputs is high(1). • 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. 2 3 4 5

Definitions of the components/Keywords: 1 • A universal gate is a gate which can implement any Boolean function without using any other gate type. • The NAND and NOR gates are universal gates. • Any circuit can be implemented with only NAND and NOR gates. • In practice, this is advantageous since NAND and NOR gates are economical and easier to fabricate and are the basic gates used in all IC digital logic families. A X = A + B B 2 Symbols and expressions used to represent logic gates: A X = A • B Input Output B 3 • NAND: • NOR: 4 5

Definitions of the components/Keywords: 1 • Description of the gates: • NAND: The NAND gate is a digital logic gate that implements AND function with a complemented (inverted) output. A LOW(0) output occurs only when all inputs are HIGH(1). When any of the inputs is LOW(0), the output will be HIGH(1). • A small circle or a bubble at the end of an AND gate is used to signify the NAND function. • The negation or the inversion is symbolized as overbar in the Boolean expression. 2 A X = A • B B 3 4 5

Definitions of the components/Keywords: • Description of the gates: • NOR: The NOR gate is a digital logic gate that implements OR function with a complemented (inverted) output. A HIGH (1) output results when all its inputs are LOW (0). When any of the inputs is HIGH(1), the output will be LOW(0). • A small circle or a bubble at the end of an OR gate is used to signify the NOR function. • The negation or the inversion is symbolized as overbar in the Boolean expression. 1 A X = A + B B 2 3 4 5

Master Layout 1 Simulation Area Control Area Output Truth Table: Input A GATE Symbol • GATE Menu • NAND • NOR • Three radio buttons • Basic concept of GATE • Electronic Logic using Switches • Mechanical Logic using bars and joints Input B 2 3 ‘1’ - input is HIGH ‘0’- input is LOW 1 0 Legend: Toggle Switch 4 Fig. A • 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 • For NAND refer slide 8 – 39 • For NOR refer slide 40 – 71 Toggle Switch: a switch that has two positions . It has a mechanism to do two things one at a time 5 **The demo itself is interactivity in this LO**

Step 1: NAND 1 Truth Table: Output Input A Input B 2 ‘1’ - input is HIGH ‘0’- input is LOW 3 1 0 Legend: 4 5

Step 2: Basic concept of the NAND gate 1 Output 0 Input A 0 • 0 2 Input B 0 3 1 0 Legend: 4 5

Step 3: 1 Output 0 Input A 1 2 Input B 0 3 1 0 Legend: 4 5

Step 4: 1 Output 0 Input A 0 • 1 2 Input B 1 3 1 0 Legend: 4 5

Step 10: NAND gate using Switches 1 Output Input A Input B 2 LED Switch open 3 Battery Switch closed ** For every combination, initially figure in slide 10 must be shown. Then depending upon the inputs corresponding switch must be closed or opened and the movement must be shown. 4 1 0 Legend: 5

Step 11: 1 Output 0 Input A Input B 0 2 Using Electronic switches 3 4 1 0 Legend: 5

Step 12: 1 Output 0 Input A 1 Input B 0 2 Using Electronic switches 3 4 1 0 Legend: 5

Step 13: 1 Output 0 Input A Input B 1 2 Using Electronic switches 3 1 0 Legend: 4 5

Step 16: 1 Output 1 Input A 1 2 Input B 0 Using Electronic switches 3 4 1 0 Legend: 5

Step 19: NAND gate using Mechanical bars and joints 1 Output Input A Input B 2 3 Refer slide 27(next slide) for figure ** For every combination of inputs, initially figure in slide 27 must be shown. Then depending upon the inputs corresponding legs must be moved and the movement must be shown 1 0 Legend: 4 5

Input A Yellow joint Red joint 0 1 Rack A Pinion / small wheel 0 1 Green joint Rack B Input B 0 1 Output • *** The animation in this slide is for visual reference but see slides 26 – 39 for more details • If any one leg is moved from 0 to 1, Rack A doesn’t move. So the output remains at 1. • If both the legs are moved from 0 to 1, Rack A moves. This makes wheel to rotate in clockwise direction and this wheel makes Rack B to move simultaneously. All the movements are shown as animation. • To view animation see in slideshow mode

Step 20: 1 Output 0 Input A Input B 0 2 3 Refer slide 29 (next slide) for figure 1 0 Legend: 4 5

Fig. A (same figure of slide 27) Input A 0 1 0 1 Input B Fig. B 0 1 Output

Step 21: 1 Output 0 Input A 1 Input B 0 2 3 Refer slide 29 (previous slide) for figure 4 1 0 Legend: 5

Input A 0 1 0 1 Input B 0 1 Output

Step 23: 1 Output 0 Input A 1 Input B 1 2 3 Refer slide 32 (previous slide) for figure 1 0 Legend: 4 5

Input A 0 1 0 1 Input B 0 1 Output

Step 25: 1 Output 1 Input A 1 Input B 0 2 3 Refer slide 35 (previous slide) for figure 4 1 0 Legend: 5

Step 26: 1 Output 1 Input A Input B 1 2 Refer slide 38 (next slide) for figure 3 1 0 Legend: 4 5

***For Input A -1 and Input B -1 combination, the animation is shown in slide 27 Input A 0 1 0 1 Input B 0 1 Output

Step 27: 1 Output 1 Input A 0 Input B 1 2 3 Refer slide 38 ( previous slide) for figure 1 0 Legend: 4 5

Step 1: NOR 1 Truth Table: Output Input A Input B 2 ‘1’ - input is HIGH ‘0’- input is LOW 3 1 0 Legend: 4 5

Step 2: Basic concept of the NOR gate 1 Output 0 Input A 0 + 0 2 Input B 0 3 1 0 Legend: 4 5

Step 4: 1 Output 0 Input A 0 + 1 2 Input B 1 3 1 0 Legend: 4 5

Step 10: NOR gate using Switches 1 Output Input A Input B 2 Switch open 3 LED Battery Switch closed ** For every combination, initially figure in slide 10 must be shown. Then depending upon the inputs corresponding switch must be closed or opened and the movement must be shown. 4 1 0 Legend: 5

Logic Gates Part – II : Universal Logic Gates