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Clemson ECE Laboratories ECE 209 – Logic and computing devices Pre-labs for ECE 209 Created: 9/4/12 by Madhabi Manandhar Last Updated: 12/20/2012 1 Clemson ECE Laboratories LABORATORY 0 – LAB INTRODUCTION 2 Clemson ECE Laboratories Outline • Syllabus highlights • Good lab procedures for ECE 201 • Hardware used in lab ECE 209 lab kit NI-ELVIS –II • Software used in the lab Digital Works • Safety video 3 Clemson ECE Laboratories Syllabus Highlights Grade Composition: 25 % Pre-lab preparation and design 25% Class performance and demonstration of functional circuits 30% Full lab reports 20% Final project and presentation Grading Scale: A: 90-100% B: 75-89% C: 60-74% D: 50-59% F: <50% 4 Clemson ECE Laboratories Syllabus Highlights (cont.) Pre-lab Preparation and Design (25% of grade): • Thoroughly read the experiment in the manual before coming to the lab. • Pre-lab reports are to be turned in before each lab and may consist of simulation(s), diagrams, truth tables, K-maps, etc. • Wiring you circuits prior to coming to lab will make the lab quicker and easier for both the student and instructor. Prewiring circuits will also reduce the chance of students not having enough time to complete the lab. 5 Clemson ECE Laboratories Syllabus Highlights (cont.) Class Performance/Functional Circuits (25% of grade): • Attend each lab and participate • Correctly wire the circuits required in the lab manual and demonstrate that the circuit functions correctly to the instructor Attendance is mandatory for every lab; however, if the instructor is not in the classroom within 15 minutes after the class is scheduled to start, then the students are free to leave (unless they have been told otherwise in advance). 6 Clemson ECE Laboratories Syllabus Highlights (cont.) Full Lab Reports (30% of grade): Throughout the semester there will be 3 full lab reports assigned, each will count as 10% of your overall grade. These reports must be typed using a word processor. Grades will be based on organization, content, neatness, accuracy, conclusions, and format. A standard format is as follows (format may vary with different instructors): • Title Page (Title, date, due date, author, lab partner(s)) • Objectives (Succinctly state the purpose of the lab) • Procedure (State what you did (circuit diagrams) and present results) • Conclusion • College of Engineering Honor Code and Signature 7 Clemson ECE Laboratories Syllabus Highlights (cont.) Final Project and Presentation (20% of grade): There is NOT A FINAL EXAM for this lab course. Instead there will be a project involving design, simulation, and analysis of a digital-circuit related to a concept of your choice. • You may work individually or in groups of 2 • One report will be required for each group • Your group will give a presentation about your project during the last lab session You will receive more information regarding this project in the second half of the semester. 8 Clemson ECE Laboratories Good lab procedures • Be very careful while wiring circuits • Don’t leave wire dangling about • Make sure all the connections are made correctly (reverse power leads can destroy your IC chips) • Before wiring always draw a circuit diagram with pin numbers and chips labeled • While wiring and rewiring turn off the power • Avoid messy wiring • Handle equipment carefully • Before leaving lab check to make sure your bench position is neat and orderly 9 Clemson ECE Laboratories Hardware – ECE 209 Lab Kit Protoboard: • Inserting IC chips on a protoboard 10 Clemson ECE Laboratories 11 Hardware – ECE 209 Lab Kit (cont.) Integrated Circuits (ICs): IC pin numbers: The position of pin 1 is determined by a dot or notch on the IC. The numbers typically increase in the counterclockwise direction (but there are exceptions). Once we know the pin numbers, we can use the chip pin-out to create our circuit. Notch Actual Chip Chip Pin-out Diagram Clemson ECE Laboratories Hardware – ECE 209 Lab Kit (cont.) Each IC chip has a number stamped on it, identifying what type of logic chip it is. For example the chip below is a 7486 logic chip which contains 4, 2-input XOR gates. Once we know the IC number, we can find the chip pin-out in pages 16-18 in the lab manual. 12 Clemson ECE Laboratories Hardware – ECE 209 Lab Kit (cont.) IC Handling: Before using the ICs we must first straighten out the legs by gently flattening the IC on a table top as shown below. Be careful, the legs/pins are very fragile. 13 Clemson ECE Laboratories Hardware – ECE 209 Lab Kit (cont.) Removing ICs: Ideally we would use an IC extractor, but we will usually just use a pencil to gently remove ICs from the protoboard. First loosen the IC on one end, and then loosen as shown below. This is to prevent the legs/pins from bending. Loosen One End of the IC Loosen Second End and Remove 14 Clemson ECE Laboratories Examples of Basic Gates – AND gate • An AND gate can be depicted by 2 switches in series Ref: http://www.technologystudent.com/pdfs/logic1.pdf 15 Clemson ECE Laboratories Examples of Basic Gates – OR gate • An OR gate can be depicted by 2 switches in parallel Ref: http://www.technologystudent.com/pdfs/logic1.pdf 16 Clemson ECE Laboratories Hardware – NI ELVIS II • • • • • • • 1: On-Off switch 2: PWR SEL Jumper 3: Power Supply 4: Logic Inputs 5: Lamp Monitors (LEDs) 6: Function Generator 7: Analog Inputs 17 Clemson ECE Laboratories Hardware – NI ELVIS II (cont.) Powering the Circuits: • For our circuits to operate the NI-ELVIS board must be turned on (there are two switches which need to be “on”, the one pictured in the previous diagram and one on the back right side of the board). • The ICs in our circuits will require Vcc (+5 V) and GND (ground) according to the pin-outs. The pins for Vcc and GND are in the “Power Supply” area of the board; area 3 in the previous slide. 18 Clemson ECE Laboratories Hardware – NI ELVIS II (cont.) Digital Inputs: • Most, if not all of our circuits will require digital inputs. i.e. inputs that are either logic 1 (+5 V) or logic 0 (GND). We could manually move a wire between the +5 V and GND pins, but it is easier to use a specialized pin that we can change between +5 V and GND with software. • The specialized pins that we will use as digital inputs to our circuits are shown in area 4 of the NI-ELVIS diagram (DI0 – DI7). 19 Clemson ECE Laboratories 20 Hardware – NI ELVIS II (cont.) Controlling Digital Inputs: • Open the “NI ELVISmx Instrument Launcher” on the computer and the following GUI will appear. • Select “DigOut” and the GUI to the right will appear. • Hit the “Run” button • Click the oval corresponding to the desired input to toggle it between +5 V and GND • DI0=oval 0, DI1=oval 1, etc. “Ovals” Clemson ECE Laboratories Software – Digital Works Simulations using Digital Works: • There is a link on the lab homepage (for 32 bit machines) as well as a link in the syllabus (for 64 bit machines) where you can download Digital Works (DW). • Using DW we can simulate circuits and determine if they are functioning how they should before actually building a circuit on our protoboard. Labeling chips and pin numbers in the simulation will also make it much easier to wire circuits in the lab. • For a basic introduction to using DW go the the “Digital Works Introduction” link on the lab homepage. 21 Clemson ECE Laboratories 22 Software – Digital Works (cont.) Run button Object Interaction Basic Logic Gates Interactive Input Annotation (labeling) LED (output) Wiring Tool Clemson ECE Laboratories 23 Software – Digital Works (cont.) The following is an example of simulating a OR gate in Digital Works Z=X+Y Clemson ECE Laboratories Contact Information • Instructor: Name: Email: Office: Phone: Office Hours: As needed (email for appointment) • Lab Coordinator: Name: Dr. Timothy Burg Email: [email protected] Office: 307 Fluor Daniel (EIB) Phone: (864)-656-1368 24 Clemson ECE Laboratories Safety Video 25 Clemson ECE Laboratories LABORATORY 1 – LOGIC GATES: A SMART LIGHTING SYSTEM 26 Clemson ECE Laboratories Introduction to Laboratory 1 • Objective: Explore notion of combinational circuits and basic combinational design • Requirements – Digital works simulation for all 3 circuits – Verbal description of the function of final circuit – Truth table for first function (the light controller) 27 Clemson ECE Laboratories Lab overview • Design a circuit that controls a light with 5 input • The light is turned on when – Burglar Alarm (B) detects an intruder – Master Light Switch (M) is on – An Auxiliary Switching system (A1, A2) is on and a Person (P) is present in the room (person detector is on) 28 Clemson ECE Laboratories Logic equation • : XOR function for auxiliary switching system • : : Person detected AND auxiliary switching system on • : Master Switch is on OR Person is detected AND Auxiliary switching system is on • Desired lighting function is 29 Clemson ECE Laboratories Building a digital light control 30 Clemson ECE Laboratories Implementing a Function with different gates • Implement the XOR function using only AND and OR gates • Simulate the circuit in digital works • Wiring the circuit is optional. 31 Clemson ECE Laboratories Realizing an Arbitrary Boolean Function • Design a circuit using only truth tables and logic function • Logic function is • Simulate and wire the circuit using AND, OR and NOT gates 32 Clemson ECE Laboratories Preparations for Next Week • Next week’s lab Encoding/Decoding: The SevenSegment Display • Requirements: – Simulation of functional seven-segment display circuit – Truth table for all seven segments and all seven functions in MSOP 33 Clemson ECE Laboratories LABORATORY 2 – ENCODING/DECODING: THE SEVEN-SEGMENT DISPLAY 34 Clemson ECE Laboratories Introduction to Laboratory 2 • Objective: Become familiar with the seven-segment LED display, encoding/decoding, and BCD (binary coded decimal) • Requirements: – Simulation of functional seven-segment display circuit – Truth table for all seven segments and all seven functions in MSOP 35 Clemson ECE Laboratories 36 Decoding/Encoding Decoding: Decoding is the conversion of a n-bit input code to a m-bit output code with n ≤ m ≤ 2n. As an example, the inputs (Ai) and the outputs (Di) for a 2-to-4 line decoder are shown below: A1 A0 D0 D1 D2 D3 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 Encoding: Encoding is the inverse operation of decoding. An encoder converts a m-bit input to a n-bit output with n ≤ m ≤ 2n. The above table would represent an encoder if the D’s were inputs and the A’s were outputs. M. M. Mano and C. R. Kime, Logic and Computer Design Fundamentals Clemson ECE Laboratories 37 Binary Coded Decimal (BCD) When converting from decimal to BCD we convert each decimal digit individually using the following table: Decimal Symbol BCD Digit 0 1 2 3 4 5 6 7 8 9 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 A decimal number in BCD is the same as its equivalent binary number only when the number is between 0 and 9 (inclusive). A BCD number greater than 10 has a representation different from its equivalent binary number. This can be seen below for the conversion of decimal 185: (185)10 = (0001 1000 0101)BCD = (10111001)2 1 8 M. M. Mano and C. R. Kime, Logic and Computer Design Fundamentals 5 Clemson ECE Laboratories Seven-Segment Display • Decimal numbers are displayed by a seven-segment display as shown in the figure • The truth table and logic function for segment A are 38 Clemson ECE Laboratories Seven-Segment Display (cont.) There are two types of seven segment displays • Common Anode (what we have) – Common connection tied to +5v – Logic low inputs used to light LED • Common Cathode – Common connections tied to ground – Logic high input lights up LED • 220 Ω resisters critical to limit current through LEDs 39 Clemson ECE Laboratories 7447 BCD to Seven-Segment Display • A truth table can be made for all of the segments, but because this function is very common, a single chip has been standardized to perform this conversion. The chip is the 7447. • The chip can be connected as follows 40 Clemson ECE Laboratories Preparation for next week • Next week’s lab - Combinational Circuits: Parity Generation and Detection • Requirements – K-map for parity generator and detector – Truth table for parity detector – Simulation of functional parity generator/detector 41 Clemson ECE Laboratories LABORATORY 3 – COMBINATIONAL CIRCUITS: PARITY GENERATION AND DETECTION 42 Clemson ECE Laboratories Introduction to Laboratory 3 • Objective: Familiarize students with combination circuits • Requirements – K-map for parity generator and detector – Truth table for parity detector – Simulation of functional parity generator/detector 43 Clemson ECE Laboratories Combinational Circuit • Circuit implemented using Boolean circuits • Uses gates exclusively, so that it deals with boolean functions • Cannot store memory – Has no provision to store past inputs and outputs • Used for doing boolean algebra in computer circuits 44 Clemson ECE Laboratories Karnaugh Map • Becomes difficult to implement larger boolean expressions More expressions -> More gates -> Complex circuit -> Difficult to connect and implement • Expressions can be reduced mathematically, but a tough nut to crack • Karnaugh Maps makes expression as simple as possible, as well as its solving process • Useful for combinational circuit – reduces the boolean expression substantially 45 Clemson ECE Laboratories Section 1 PARITY GENERATORS 46 Clemson ECE Laboratories Parity Generator • Used to detect whether the number of 1s in the input is even or odd, indicated by a parity bit • Used for detecting errors in the received data • Two types: 1. Even parity – Parity bit -> high, when 1s -> odd. Makes total number of 1s even in the set 2. Odd Parity – Parity bit -> high, when 1s ->even. Makes total number of 1s odd in the set 47 Clemson ECE Laboratories 48 Parity Generator contd… • By your knowledge so far, along with new information, what do you think is the basic parity generator? And what type? • How parity bits are used (Even Parity): 1 0 0 1 1 1 1 1 0 1 1 0 PARITY BIT PARITY BIT PARITY BIT Clemson ECE Laboratories Parity generator contd… • For an odd parity generator with three inputs and one output, the truth table is X Y Z P 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 49 Clemson ECE Laboratories 50 Parity generator contd.. • K-Map for Odd Parity Generator Y’Z’ Y’Z YZ YZ’ X’ 1 0 1 0 X 0 1 0 1 P = X’Y’Z’ + XY’Z + X’YZ +XYZ’ Clemson ECE Laboratories Parity Generator contd… P = X’Y’Z’ + XY’Z + X’YZ +XYZ’ P = [X’(Y’Z’+YZ)] + [X(Y’Z + YZ’)] P = [X’ AND (Y⊕Z)’] + [X AND (Y⊕Z)] Original Number of 2-input gates (4 x NOT) + (6 x AND) + (4 x OR) = 14 gates Number of 2-input Gates for the highlighted expression (2 x NOT) + (1 x XOR) + (2 x AND) + (1 x OR) = 6 gates 51 Clemson ECE Laboratories Parity Generator contd… 6 Gates sound too much still, isn’t it? Let’s check the highlighted equation again: P = [X’ AND (Y⊕Z)’] + [X AND (Y⊕Z)] Let (Y⊕Z) = W P = [X’ AND W’] + [X AND W] P = X’W’ + XW What does this remind you of? P = X XNOR W => P = (X ⊕ W)’ Replacing the value of W P = (X ⊕ Y ⊕ Z)’ Number of 2-input gates now => (2 x XOR) + (1 x NOT) => 3 gates! 52 Clemson ECE Laboratories Section 2 PARITY DETECTORS 53 Clemson ECE Laboratories Parity detector • No use of parity generators, if there’s nothing to acknowledge – or check for – the parity bits • Chances exist of noise in data sent over a communication channel • Errors detected using parity detectors • Parity generator and detector go hand-in-hand 54 Clemson ECE Laboratories Parity detector contd… • Odd parity detector for 3 inputs 55 Clemson ECE Laboratories 56 Parity detector contd… • K-Map for Odd parity detector Z’P’ Z’P X’Y’ X’Y XY XY’ ZP ZP’ Clemson ECE Laboratories Parity detector contd… E = (X ⊕ Y ⊕ Z ⊕ P )’ Number of 2-input Gates for the highlighted expression (3 x XOR) + (1 x NOT) = 4 gates 57 Clemson ECE Laboratories Parity generator and detector • Create parity generator and detector circuits and connect them as shown in the figure below • Also simulate a communication where a single bit error is introduced to any of the four inputs to parity detector 58 Clemson ECE Laboratories Lab Report • Due Next Lab • Objective – Goal of the lab • Split the report into two parts here • Just mention the parts, and start from the same page. No need for separate pages to indicate separate parts. 59 Clemson ECE Laboratories Lab Report contd… Part 1: Parity Generator • Schematic Diagram – One will suffice • Explanation i. What is a Parity Generator? ii. Truth Table iii. K-Map iv. Derive the equation that you used in the lab v. Importance • Result – Explain your result as you understood 60 Clemson ECE Laboratories Lab Report contd… Part 2: Parity Detector • Schematic Diagram – One will suffice. You can show “P” as an input. No need to attach parity generator circuit to it. • Explanation i. What is a Parity Detector? ii. Truth Table iii. K-Map iv. Derive the equation that you used in the lab v. Importance • Result – Explain your result as you understood 61 Clemson ECE Laboratories Lab Report contd… • Conclusions – Write the conclusion based on your experience while working with K-maps, gates, and parity-generator and –detector. • Honor Code – Limit to one important paragraph 62 Clemson ECE Laboratories Preparation for next week • Read about binary arithmetic and properties • Learn more about K-maps, and how they are used to reduced the number of elements in the expression • Understand binary half-adders and full-adders, and difference between them • Generate truth tables for half- and full-adders • Though half-adder is not mentioned in the labmanual, we’ll be doing it the next class 63 Clemson ECE Laboratories LABORATORY 4 – BINARY ARITHMETIC - ADDERS 64 Clemson ECE Laboratories Introduction to Laboratory 4 • Objective: Demonstrate knowledge of simple binary arithmetic and mechanics of its use • Requirements – Simulation of functional Full Adder 65 Clemson ECE Laboratories 66 Half Adder • When 2 single bits A and B are added the truth table and Kmaps for this operation are as follows: Sum (S) B 0 1 0 0 1 1 1 0 A Carry (C) B 0 1 0 0 0 1 0 1 A • From the truth table and or K-maps we can determine that the functions for C and S are as shown below. Clemson ECE Laboratories Half Adder (cont.) • Now consider the addition of two 8-bit binary numbers: • We can see that we are actually adding three bits, two bits from the numbers being added and one additional carry bit. • Since the half adder does not take this carry bit (Cin) into consideration a new model is needed. This new model is a full adder. 67 Clemson ECE Laboratories 68 Full Adder • The truth table and K-maps for the full adder are shown below. Sum (S) AB Carry Out (Cout) 00 01 11 10 0 0 1 0 1 1 1 0 1 0 Cin AB 00 01 11 10 0 0 0 1 0 1 0 1 1 1 Cin • The familiar checkerboard pattern in S and the circled groups in Cout lead to the full adder functions that are shown below. Clemson ECE Laboratories Full Adder (cont.) • A circuit diagram which creates the sum (S) and carry (Cout) bits of a full adder is shown below. 69 Clemson ECE Laboratories Building 2-bit Full Adder • Two full adders can be combined to make a 2-bit adder as shown in the diagram below • Build a 2-bit adder on your bread-board and test the circuit 70 Clemson ECE Laboratories Preparation for next week • Next week’s lab: MSI Circuits – Four-Bit Adder/Subtractor with Decimal Output • Requirements – Simulation of functional circuit 71 Clemson ECE Laboratories LABORATORY 5 – MSI CIRCUITS – FOUR-BIT ADDER/SUBTRACTOR WITH DECIMAL OUTPUT 72 Clemson ECE Laboratories Introduction to Laboratory 5 • Objective: Familiarize students with MSI technology, specifically adders and also 1’s complement arithmetic • Requirements – Simulation of functional Full Adder 73 Clemson ECE Laboratories Representation of Negative Numbers as Binary • Ideally, a binary number is represented in an “exponential of 2” number of bits, i.e. 2, 4, 8, 16 … • Three types of negative-number representation. Interested only in 1’s complement, i.e. complementing of every bit of the original number to get negative counterpart • E.g. 4- bit 1’s Complement 8-bit 1’s complement 7 – 0111 10 - 00001010 -7 – 1000 -10 – 1111010 • Why is it known as 1’s complement? Because it is obtained by subtracting the unsigned number from 0’s complement. Try it yourself. 74 Clemson ECE Laboratories 4-Bit Adder & Subtractor • The 7483 chip is a 4 bit full adder • Subtraction is addition of a positive and a negative number • Apart from addition, the chip can be used for 1’s complement subtraction 75 Clemson ECE Laboratories 76 Example of 1’s complement subtraction – – – – Take 1’s complement of 1 i.e. (-1) Add (-1) to 7 Add the carry bit to the result Result of addition is the final result Ref: Wikipedia Clemson ECE Laboratories 77 Building 1’s Complement Subtractor • Take 1’s complement using complement a bit when input is 1 • Why not NOT gate? XOR gates Input to determine the nature of adder 0: Addition 1:Subtraction to Clemson ECE Laboratories Steps for 1’s compliment subtraction • If the numbers are in decimal-form, convert them to binary • Take 1’s complement of the subrahend. • Add the 1’s complement to minuend • Instead of keeping carry bit as the extended form of difference, add it to the answer • S4 S3 S2 S1 is the final answer for add/subtract 78 Clemson ECE Laboratories 79 Clemson ECE Laboratories Part II use 7-segment display • Display the result in 7-segment display • Use the 7447 chip • Note : Main circuit does not contain the 4 XOR gates just before the 7447 chip 80 Clemson ECE Laboratories 81 Clemson ECE Laboratories Lab Report – Due Next Lab • • • • Objective – Goal of the lab Equipment used Split the report into two parts here Just mention the parts, and start from the same page. No need for separate pages to indicate separate parts. 82 Clemson ECE Laboratories Lab Report (cont.) Part 1: 1-bit Full Adder • Schematic Diagram – DigitalWorks • Explanation i. What is a Full Adder? ii. Truth Table iii. K-Map iv. Mention the equation that you used in the lab 83 Clemson ECE Laboratories Lab Report (cont.) Part 2: 4-bit Subtractor • Schematic Diagram - DigitalWorks • Explanation i. Concept of 1’s complement subtraction ii. A short statement on MSI chip and the one used here iii. Explanation for circuit used, including the usage of gates, resistors, BCD-to-decimal converter, and LED display iv. Truth table for LED display and BCD-to-decimal converter 84 Clemson ECE Laboratories Lab Report (cont.) • Result – Answer the questions mentioned in the lab manual • Conclusions – Write the conclusion based on your experience while working with K-maps, gates, and parity-generator and –detector. • Honor Code – Limit to one important paragraph 85 Clemson ECE Laboratories Preparation for next week • Next week’s lab : Multiplexers and Serial Communication • Requirements – Simulation of functional circuit 86 Clemson ECE Laboratories LABORATORY 6 – MULTIPLEXERS AND SERIAL COMMUNICATION 87 Clemson ECE Laboratories Introduction to Laboratory 6 • Objective: Familiarize students with internal realization of multiplexers and show an application of multiplexers and demultiplexers in serial communications • Requirements – Simulation of functional circuit 88 Clemson ECE Laboratories Multiplexer • A multiplexer is a combinational circuit that selects binary information from 2n input lines and directs the information to a single output line by using n select lines • The lab manual gives the analogy of a rotary switch like in the above figure. This is an accurate comparison but note that there is not an actual switch in the multiplexers. • The input line that is connected to the output line is determined by the select lines (S0 and S1) and logic gates. 89 Clemson ECE Laboratories 90 Multiplexer (cont.) D0 D1 D D1023 D2 D3 1 0 0 1 Clemson ECE Laboratories Multiplexer (cont.) Why do we need multiplexers? Less Power Consumption in Displays • The lab manual gives the example of multiplexing the sevensegment displays of a calculator to reduce power usage and therefore increase battery life • What about LED advertisement boards being viewed in slow motion? Communication Systems • When there are several independent inputs which need to travel over the same line. • Consider the arrangement of phone lines. 91 Clemson ECE Laboratories Demultiplexer • A demultiplexer is another type of combinational circuit. • The function of a demultiplexer is opposite to the function of a multiplexer. • The demultiplexer takes a single input line and sends it to one of 2n output lines depending on the value of the n select lines. 92 Clemson ECE Laboratories Demultiplexer (cont.) Since we do not have a 1-to-8 demultiplexer, we will have to create one from the 74155 chip. The 74155 contains two 1-to-4 demultiplexers. To do this, make the following connections: Connect “Strobe GA” and “Strobe GB” together Input line Connect “Data CA” and “Data CB” together 3rd select line Note: The notation for the figures in the lab manual does not match exactly with the pinouts for the chips! 93 Clemson ECE Laboratories Application of multiplexer/demultiplexer • Connect the following circuit to multiplex the segments of the seven-segment display with a serial communication line. • Connect “clock” of the 74193 to the function generator of the NI ELVIS board. Use a square waveform with a Vpp of 3 volts. 94 Clemson ECE Laboratories Preparation for next week • Next week’s lab : Four – Bit Combinational Multiplier • Requirements – Simulation of functional circuit 95 Clemson ECE Laboratories LABORATORY 7 – FOUR-BIT COMBINATIONAL MULTIPLIER 96 Clemson ECE Laboratories Introduction to Laboratory 7 • Objective: Practice the combinational design process through the design of a 4-bit multiplier • Requirements – Simulation of functional circuit – No wiring necessary for this lab 97 Clemson ECE Laboratories 4 bit multiplication • Example of a 4 bit multiplication • The individual multiplication can be obtained by the AND operation and 4-bit adder can be used for addition 98 Clemson ECE Laboratories Complete multiplication • Sij represents the jth output of the ith adder • S05 , S16 and S7 are carry from the 4 bit adder • Only 4 bit adders are needed for addition as P00, S01 and S12 are directly given to the output 99 Clemson ECE Laboratories Preparation for next week • Next week’s lab : Logic Design for a Direct-Mapped Cache • Requirements – Simulation of functional circuit along with all the macros used 100 Clemson ECE Laboratories LABORATORY 8 – LOGIC DESIGN FOR A DIRECTMAPPED CACHE 101 Clemson ECE Laboratories Introduction to Laboratory 8 • Objective: Understand the function and design of a direct-mapped cache • Requirements – Simulation of functional circuit along with all the macros used – No wiring necessary for this lab 102 Clemson ECE Laboratories Terminology 1 Byte = 8 bits (i.e. 1001 0110 is one byte) 1 kilobyte (kB) = 210 bytes = 1,024 bytes (as opposed to the equality: 1 kilometer = 103 meters = 1,000 meters) 1 megabyte (MB) = 220 bytes = 1,048,576 bytes (as opposed to the equality: 1 megameter = 106 meters = 1,000,000 meters) 1 gigabyte (GB) = 230 bytes = 1,073,741,824 bytes (as opposed to the equality: 1 gigameter = 109 meters = 1,000,000,000 meters) 103 Clemson ECE Laboratories 104 Background • The CPU requires data from memory (instructions for programs and numerical data) • When a computer needs to read from memory it generates a memory address Basic Computer Organization • The next step is to locate where the data associated with the address is currently residing • The first memory it checks is the cache, if it is there it is a cache hit, otherwise it is a miss A. S. Tanenbaum, Structured Computer Organization Clemson ECE Laboratories Background (cont.) few ns (10-9 s)/~100 bytes few ns (10-9 s)/few megabytes tens of ns (10-9 s)/thousands of megabytes tens of ms (10-3 s)/few gigabytes several seconds/limited only by budget (kept separate) Moving Down the Pyramid 1. Longer access times (slower) 2. Increased storage capacity (larger) 3. Cost per bit decreases (cheaper) A. S. Tanenbaum, Structured Computer Organization • Data most frequently needed is kept in small, fast, but expensive memory. • Less frequently needed data is kept in large, slow, and cheap memory. 105 Clemson ECE Laboratories 106 Direct-mapped cache The goal of this lab will be to develop logic which determines whether or not the required data is in the cache (the output will indicate whether we have a cache hit or a miss). Our fictional computer is characterized by the following: • 16 bit address bus 216 = 210*26 = 1 kB*64 = 64 kB (total memory) • 16 line cache with 256 bytes each 256 B*16 = 28*24 = 210*22 = 1 kB*4 = 4 kB (data from memory that can be stored in the cache) Line1,byte1 Line1,byte2 Line1,byte3 Line1,byte4 Line2,byte1 Line2,byte2 Line2,byte3 Line2,byte4 Line3,byte1 Line3,byte2 Line3,byte3 Line3,byte4 Line4,byte1 .. . Line4,byte2 .. . Line4,byte3 .. . Line4,byte4 ... ... ... ... Line16,byte1 Line16,byte2 Line16,byte3 Line16,byte4 ... .. . Cache Structure Line1,byte256 Line2,byte256 Line3,byte256 .. . Line4,byte256 Line16,byte256 Clemson ECE Laboratories Direct-mapped cache (cont.) • The 16 bit memory address is arranged as shown (Offset) • Cache line address indicates which line in the cache the address will be in • Tag tells us which block is present 107 Clemson ECE Laboratories Example One block • Only memory addresses whose cache line address field matches can be in a particular cache (only one block per cache line). 108 Clemson ECE Laboratories Lab Procedure • We will not be concerned with the “offset” bits. • We will be working with the “tag” bits of the address which are stored in a tag memory that is associated with the cache. • We will also be working with a “valid” bit in the tag memory which indicates if the information in the cache is valid. 109 Clemson ECE Laboratories Lab Procedure (cont.) • Based on the information in the previous slides, we will need a 16x5 tag memory. We will implement the tag memory in Digital Works using ROM (initialized according to the table to the right). • Inputs to the ROM will be the “cache line address bits” and the “tag” bits of the memory address (i.e. you will need 8 inputs in your simulation). • The “cache line address” bits will determine which line in the cache to retrieve the tag from. The retrieved tag bits will then be compared with the tag bits in the memory address. • Use a comparator to turn on an LED if the retrieved tag bits are the same as the tag bits in the memory address and the valid bit is a one. 110 Clemson ECE Laboratories Note on comparators The XNOR function can be used to compare 2 bits Two 4-bit binary numbers are the same if and only if the two 1st bits are equivalent and the two 2nd bits are equivalent and the two 3rd bits are equivalent and the two 4th bits are equivalent 111 Clemson ECE Laboratories Preparation for next week • Next week’s lab : Understand the design and restrictions of Sequential Circuits • Requirements – Simulation of functional circuit 112 Clemson ECE Laboratories LABORATORY 9 – SEQUENTIAL DESIGN – THREE BIT COUNTER 113 Clemson ECE Laboratories Introduction to Laboratory 9 • Objective: Understand the design and restrictions of Sequential Circuits • Requirements Electronic copy of your design. Schematic of final design. State Transition Tables. Karnaugh Maps with Boolean reductions for each variable. 114 Clemson ECE Laboratories 115 Sequential Circuit • Some circuits need the knowledge of present – as well as past – inputs, along with the outputs it had generated last time. • Combinational circuit can’t be used, as it uses only present inputs, and thus has no memory • Sequential circuit comes in handy in such situations • The output state of a "sequential logic circuit" depends on: Present Input; Past input; and Past output • In general, combinational circuit is a type of sequential circuit • Applications: Timers, counters, memory-management, etc. Vital for building larger and more complex electronic circuits, such as robots, computers, and digital watches. Clemson ECE Laboratories Flip-flops • Flip-flop is the basic form of a sequential circuit • It uses outputs derived from previous inputs to determine the output from the current inputs • Types of flip-flops: J-K Flipflop S-R Flipflop D Flipflop T Flipflop 116 Clemson ECE Laboratories Three-bit counter • Counter – Basic form of sequential circuit • Starts counting from 0-higher number – or highernumber-0 – once signal is given to the circuit • Requires 4 flipflops to get 3-bit counting (will use D flipflop for this lab) • Inputs: c (c = 0 =>up-count; c=1 =>down-count) • Inputs from previous operations: Q1, Q2, Q3 • Outputs: Q1, Q2, and Q3 117 Clemson ECE Laboratories Logic equations for 3 inputs to D flip flop • • • • c=0 means count up, c=1 means count down D1 can be easily implemented D2 can be realized using just 2 XOR gates Factor out c and c’ to obtain a simple form 118 Clemson ECE Laboratories Implementing D3 using JK flip flop • Simplifying D3 • Comparing equation of D3 with the logic equation of a JK flip flop gives the input to the JK flip flop 119 Clemson ECE Laboratories THE END 120