Problem Set 4 Solutions
|
|
- Chrystal Evans
- 6 years ago
- Views:
Transcription
1 SE 26 igital omputers: Organization and Logical esign Jon Turner Problem Set 4 Solutions 1. Find a minimal logic expression for the NN/NOR circuit shown below. The circuit implements the expression ((() + ) + ) = (( + + ) + ) = (+ ) = (+ ) = ( + ) = + 2. Give an equivalent N/OR circuit, corresponding to the NN/NOR circuit shown below. The circuit at left below was obtained by re-drawing the NOR gates in the alternate form. The circuit at right was obtained by cancelling redundant inversions and replacing others with inverters
2 This makes it obvious that the function implemented by this circuit is ( ), allowing us to simplify the circuit further to the one shown below. 3. How many transistors are used by original circuit in the previous problem? How many are used by the circuit in your solution? The original circuit had four NNs and NORs, plus an inverter, giving 18 transistors. The first of the two solution circuits has four N/OR gates, plus two inverters, giving 28 transistors. The final solution has Find a less-expensive NN/NOR equivalent for the circuit below. ompare the number of transistors used by the two circuits. The NN/NOR circuit appears at right. This circuit has =22 transistors, vs =28 transistors for the original circuit
3 5. The and function is associative. That is ( and ) and = and ( and ). What about the nand function? Justify your answer. ased on your answer, show would you implement a nand function with 8 inputs, using just simple NN and NOR gates (that is, gates with 2 inputs) and inverters. If a NN or NOR gate has a delay of 2 and an inverter has a delay of 1, what is the worst-case propagation delay for your gate implementation? ompare the delay for your circuit to the delay for an eight input NN gate implemented directly in MOS transistors (generalize the NN3 on page 4.11 of the notes). lso, compare the transistor counts for the two circuits. The nand function is not associative, since ( nand ) nand = (() ) = +, while nand ( nand ) = (() ) = + and these are clearly not equal. The figure below shows one way to implement an eight input nand function with simple NN and NOR gates. This circuit has NOR gates in the center stage and has a delay of 6 ns. If we were to implement the NN function directly, using an eight input gate, the delay would be 8 ns (since there are eight pull-downs in series, making the falling transition four times slower than the 2 input gate). The transistor counts for the two circuits are 28 and 16 respectively, so the direct implementation is uses significantly fewer transistors at the cost of a relatively small increase in delay
4 6. Find a circuit using the minimum number of 4 input LUTs that implements the three logic equations shown below. = ( + F )( + E) Y = ( + E ) + ( + + F) = ( + E)( + F) If we let U = ( + E) = ( + E ) = ( + E), we can re-write the above expressions as = ( + F )U Y = U + ( + + F) = U( + F) Note that each of these expressions involves just four variables,,, F and U. So, we can use one LUT to implement U and three more to implement the outputs, Y and giving a total of four. The resulting circuit is E P Q R S LUT4 PQ + PQ R U F P Q R S LUT4 (P+QR )S P Q LUT4 R S S +(P Q+PQ +QR) Y P Q R S LUT4 PS(Q +P R) - 4 -
5 7. onsider the circuit shown below. Suppose this circuit is implemented directly, using MOS, with each N gate implemented using a NN and an inverter (similarly for OR gates). What is the worst-case delay for the circuit, assuming that NN and NOR gates have a delay of 1 ns each, and inverters have a delay of.5 ns? Highlight the path through the circuit that accounts for the worst-case delay. U V F G Y The worst-case delay is 5 ns for the highlighted path. Show an alternate implementation, using NNs, NORs and inverters that reduces the delay by at least 1.5 ns. U V F G Y This circuit has a worst-case delay of 3.5 ns from Y to F and from Y to G
6 8. onsider the circuit shown below. ssume that all gates have a minimum propagation delay (for both rising and falling edges) of 1 ns, and a maximum propagation delay of 2 ns. onstruct two timing diagrams showing how all the labeled signals change when input changes from 1 to, while inputs and are held at 1 and, respectively. In the first timing diagram, assume the minimum propagation time for all gates and in the other, assume the maximum propagation time for all gates. raw a third timing diagram which combines the first two, using shading to show the time periods where signal values could be either or 1. uncertainty region
7 9. esign circuits that implement the logic in the truth table shown below. esign two circuits, one which has the smallest possible worst-case propagation delay, and a second which minimizes the gate count. Use only inverters and 2-input N gates and 2-input OR gates. ssume each inverter has a propagation delay of 1 ns and each N and OR gate has a 2 ns propagation delay. When counting gates, treat an inverter as a half-gate. What are the gate counts and worst-case propagation delays for your circuits? = + + = ((+ ) + ) = + + = (+)(+ + ) The first circuit shown corresponds directly to the minimum sum-of-products form of the logic expression and the second to a factorization of the sum-of-products. The first has a gate count of 9 and a worst-case propagation delay of 8 ns, while the second has a gate count of 6 and a worst-case - 7 -
8 propagation delay of 9 ns. However, if we cover the zeros in the K-map to obtain the product-of-sums form, we get a simpler expression, which results in the last circuit shown. This has a gate count of 6 and a worst-case propagation delay of 7 ns, so it is both smallest and fastest. 1. onsider the circuit and timing diagram shown below. ssuming that the inverters are all implemented using MOS technology the output signals and are both a single gate input, which of the two curves labeled with a question mark corresponds to the signal and which to signal? ssume that all the inverters are identical. Explain why this is true.?? The first one corresponds to signal and the second one to signal. The reason for this is that the pull-ups in the pair of inverters driving signal act like a pair of parallel resistors when the input is low. This allows them to pass twice as much current as a single resistor would, so they can pump charge into the output faster, causing the voltage to rise faster
12/31/2010. Overview. 10-Combinational Circuit Design Text: Unit 8. Limited Fan-in. Limited Fan-in. Limited Fan-in. Limited Fan-in
Overview 10-ombinational ircuit esign Text: Unit 8 Gates with elays and Timing Other Hazards GR/ISS 201 igital Operations and omputations Winter 2011 r. Louie 2 Practical logic gates are limited by the
More informationCombinational Logic Design
PEN 35 - igital System esign ombinational Logic esign hapter 3 Logic and omputer esign Fundamentals, 4 rd Ed., Mano 2008 Pearson Prentice Hall esign oncepts and utomation top-down design proceeds from
More informationProblem Set 9 Solutions
CSE 26 Digital Computers: Organization and Logical Design - 27 Jon Turner Problem Set 9 Solutions. For each of the sequential circuits shown below, draw in the missing parts of the timing diagrams. You
More informationWorking with Combinational Logic. Design example: 2x2-bit multiplier
Working with ombinational Logic Simplification two-level simplification exploiting don t cares algorithm for simplification Logic realization two-level logic and canonical forms realized with NNs and NORs
More informationChapter 9. Estimating circuit speed. 9.1 Counting gate delays
Chapter 9 Estimating circuit speed 9.1 Counting gate delays The simplest method for estimating the speed of a VLSI circuit is to count the number of VLSI logic gates that the input signals must propagate
More informationVLSI Circuit Design (EEC0056) Exam
Mestrado Integrado em Engenharia Eletrotécnica e de omputadores VLSI ircuit esign (EE0056) Exam 205/6 4 th year, 2 nd sem. uration: 2:30 Open notes Note: The test has 5 questions for 200 points. Show all
More informationCombinational Logic (mostly review!)
ombinational Logic (mostly review!)! Logic functions, truth tables, and switches " NOT, N, OR, NN, NOR, OR,... " Minimal set! xioms and theorems of oolean algebra " Proofs by re-writing " Proofs by perfect
More informationChapter # 3: Multi-Level Combinational Logic
hapter # 3: Multi-Level ombinational Logic ontemporary Logic esign Randy H. Katz University of alifornia, erkeley June 993 No. 3- hapter Overview Multi-Level Logic onversion to NN-NN and - Networks emorgan's
More informationChapter 3 Combinational Logic Design
Logic and Computer Design Fundamentals Chapter 3 Combinational Logic Design Part 1- Implementation Technology and Logic Design Overview Part 1-Implementation Technology and Logic Design Design Concepts
More informationComputer Organization I. Lecture 13: Design of Combinational Logic Circuits
Computer Organization I Lecture 13: Design of Combinational Logic Circuits Overview The optimization of multiple-level circuits Mapping Technology Verification Objectives To know how to optimize the multiple-level
More informationMealy & Moore Machines
Mealy & Moore Machines Moore Machine is a finite-state machine whose output values are determined solely by its current state and can be defined as six elements (S, S 0, Σ, Λ, T, G), consisting of the
More informationFloating Point Representation and Digital Logic. Lecture 11 CS301
Floating Point Representation and Digital Logic Lecture 11 CS301 Administrative Daily Review of today s lecture w Due tomorrow (10/4) at 8am Lab #3 due Friday (9/7) 1:29pm HW #5 assigned w Due Monday 10/8
More informationLearning Objectives. Boolean Algebra. In this chapter you will learn about:
Ref. Page Slide /78 Learning Objectives In this chapter you will learn about: oolean algebra Fundamental concepts and basic laws of oolean algebra oolean function and minimization Logic gates Logic circuits
More informationVLSI Design, Fall Logical Effort. Jacob Abraham
6. Logical Effort 6. Logical Effort Jacob Abraham Department of Electrical and Computer Engineering The University of Texas at Austin VLSI Design Fall 207 September 20, 207 ECE Department, University of
More informationECE 342 Electronic Circuits. Lecture 34 CMOS Logic
ECE 34 Electronic Circuits Lecture 34 CMOS Logic Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jesa@illinois.edu 1 De Morgan s Law Digital Logic - Generalization ABC... ABC...
More informationUniversity of California at Berkeley College of Engineering Department of Electrical Engineering and Computer Sciences
University of California at Berkeley College of Engineering Department of Electrical Engineering and Computer Sciences EECS151/251A V. Stojanovic, J. Wawrzynek Fall 2015 10/13/15 Midterm Exam Name: ID
More information12/31/2010. Overview. 05-Boolean Algebra Part 3 Text: Unit 3, 7. DeMorgan s Law. Example. Example. DeMorgan s Law
Overview 05-oolean lgebra Part 3 Text: Unit 3, 7 EEGR/ISS 201 Digital Operations and omputations Winter 2011 DeMorgan s Laws lgebraic Simplifications Exclusive-OR and Equivalence Functionally omplete NND-NOR
More informationDesigning Information Devices and Systems II Fall 2017 Miki Lustig and Michel Maharbiz Homework 1. This homework is due September 5, 2017, at 11:59AM.
EECS 16 Designing Information Devices and Systems II Fall 017 Miki Lustig and Michel Maharbiz Homework 1 This homework is due September 5, 017, at 11:59M. 1. Fundamental Theorem of Solutions to Differential
More informationCMOS Digital Integrated Circuits Lec 10 Combinational CMOS Logic Circuits
Lec 10 Combinational CMOS Logic Circuits 1 Combinational vs. Sequential Logic In Combinational Logic circuit Out In Combinational Logic circuit Out State Combinational The output is determined only by
More informationEEC 118 Lecture #6: CMOS Logic. Rajeevan Amirtharajah University of California, Davis Jeff Parkhurst Intel Corporation
EEC 118 Lecture #6: CMOS Logic Rajeevan mirtharajah University of California, Davis Jeff Parkhurst Intel Corporation nnouncements Quiz 1 today! Lab 2 reports due this week Lab 3 this week HW 3 due this
More informationDigital Circuits. 1. Inputs & Outputs are quantized at two levels. 2. Binary arithmetic, only digits are 0 & 1. Position indicates power of 2.
Digital Circuits 1. Inputs & Outputs are quantized at two levels. 2. inary arithmetic, only digits are 0 & 1. Position indicates power of 2. 11001 = 2 4 + 2 3 + 0 + 0 +2 0 16 + 8 + 0 + 0 + 1 = 25 Digital
More informationHomework Assignment #1 Solutions EE 477 Spring 2017 Professor Parker
Homework Assignment #1 Solutions EE 477 Spring 2017 Professor Parker Note: + implies OR,. implies AND, ~ implies NOT Question 1: a) (4%) Use transmission gates to design a 3-input OR gate Note: There are
More informationFor smaller NRE cost For faster time to market For smaller high-volume manufacturing cost For higher performance
University of California at Berkeley College of Engineering Department of Electrical Engineering and Computer Sciences EECS5 J. Wawrzynek Spring 22 2/22/2. [2 pts] Short Answers. Midterm Exam I a) [2 pts]
More informationBoolean algebra. Examples of these individual laws of Boolean, rules and theorems for Boolean algebra are given in the following table.
The Laws of Boolean Boolean algebra As well as the logic symbols 0 and 1 being used to represent a digital input or output, we can also use them as constants for a permanently Open or Closed circuit or
More informationEE371 - Advanced VLSI Circuit Design
EE371 - Advanced VLSI Circuit Design Midterm Examination May 1999 Name: No. Points Score 1. 20 2. 24 3. 26 4. 20 TOTAL / 90 In recognition of and in the spirit of the Stanford University Honor Code, I
More informationEE 330 Lecture 6. Improved Switch-Level Model Propagation Delay Stick Diagrams Technology Files
EE 330 Lecture 6 Improved witch-level Model Propagation elay tick iagrams Technology Files Review from Last Time MO Transistor Qualitative iscussion of n-channel Operation Bulk ource Gate rain rain G Gate
More informationChapter 1: Logic systems
Chapter 1: Logic systems 1: Logic gates Learning Objectives: At the end of this topic you should be able to: identify the symbols and truth tables for the following logic gates: NOT AND NAND OR NOR XOR
More informationNTE4501 Integrated Circuit CMOS, Dual 4 Input NAND Gate, 2 Input NOR/OR Gate, 8 Input AND/NAND Gate
NTE4501 Integrated Circuit CMOS, Dual 4 Input NAND Gate, 2 Input NOR/OR Gate, 8 Input AND/NAND Gate Description: The NTE4501 is a triple gate device in a 16 Lead DIP type package constructed with MOS P
More informationDigital Integrated Circuits A Design Perspective
igital Integrated Circuits esign Perspective esigning Combinational Logic Circuits 1 Combinational vs. Sequential Logic In Combinational Logic Circuit Out In Combinational Logic Circuit Out State Combinational
More informationEEC 116 Lecture #5: CMOS Logic. Rajeevan Amirtharajah Bevan Baas University of California, Davis Jeff Parkhurst Intel Corporation
EEC 116 Lecture #5: CMOS Logic Rajeevan mirtharajah Bevan Baas University of California, Davis Jeff Parkhurst Intel Corporation nnouncements Quiz 1 today! Lab 2 reports due this week Lab 3 this week HW
More informationLogical Effort. Sizing Transistors for Speed. Estimating Delays
Logical Effort Sizing Transistors for Speed Estimating Delays Would be nice to have a back of the envelope method for sizing gates for speed Logical Effort Book by Sutherland, Sproull, Harris Chapter 1
More informationProperties of CMOS Gates Snapshot
MOS logic 1 Properties of MOS Gates Snapshot High noise margins: V OH and V OL are at V DD and GND, respectively. No static power consumption: There never exists a direct path between V DD and V SS (GND)
More informationCombinational logic. Possible logic functions of two variables. Minimal set of functions. Cost of different logic functions.
Combinational logic Possible logic functions of two variables Logic functions, truth tables, and switches NOT, ND, OR, NND, NOR, OR,... Minimal set xioms and theorems of oolean algebra Proofs by re-writing
More informationEGC221: Digital Logic Lab
Division of Engineering Programs EGC221: Digital Logic Lab Experiment #1 Basic Logic Gate Simulation Student s Name: Student s Name: Reg. no.: Reg. no.: Semester: Fall 2016 Date: 07 September 2016 Assessment:
More informationOverview. Programmable logic (PLAs & PALs ) Short-hand notation. Programming the wire connections
Overview Programmable logic (PLs & PLs ) Last lecture "Switching-network" logic blocks Multiplexers/selectors emultiplexers/decoders Programmable logic devices (PLs) Regular structures for 2-level logic
More informationProblem Set 6 Solutions
CS/EE 260 Digital Computers: Organization and Logical Design Problem Set 6 Solutions Jon Turner Quiz on 2/21/02 1. The logic diagram at left below shows a 5 bit ripple-carry decrement circuit. Draw a logic
More informationAdvanced Digital Logic Design EECS 303. Multi-level example. Two-level form. Multi-level form A B C. Multi-level logic
dvanced igital Logic esign S 33 http://ziyang.eecs.northwestern.edu/eecs33/ Multi-level example Teacher: Robert ick Office: L477 Tech mail: dickrp@northwestern.edu Phone: 847 467 2298 So far, we have talked
More informationCombinational logic. Possible logic functions of two variables. Minimal set of functions. Cost of different logic functions
ombinational logic Possible logic functions of two variables asic logic oolean algebra, proofs by re-writing, proofs by perfect induction Logic functions, truth tables, and switches NOT, N, OR, NN,, OR,...,
More informationLogic Gates and Boolean Algebra
Logic Gates and oolean lgebra The ridge etween Symbolic Logic nd Electronic Digital Computing Compiled y: Muzammil hmad Khan mukhan@ssuet.edu.pk asic Logic Functions and or nand nor xor xnor not 2 Logic
More informationECE429 Introduction to VLSI Design
ECE429 Introduction to VLSI Design Lecture 5: LOGICAL EFFORT Erdal Oruklu Illinois Institute of Technology Some of these slides have been adapted from the slides provided by David Harris, Harvey Mudd College
More informationCMSC 313 Lecture 18 Midterm Exam returned Assign Homework 3 Circuits for Addition Digital Logic Components Programmable Logic Arrays
MS 33 Lecture 8 Midterm Exam returned Assign Homework 3 ircuits for Addition Digital Logic omponents Programmable Logic Arrays UMB, MS33, Richard hang MS 33, omputer Organization & Assembly
More informationDigital Electronics Final Examination. Part A
Digital Electronics Final Examination Part A Spring 2009 Student Name: Date: Class Period: Total Points: /50 Converted Score: /40 Page 1 of 13 Directions: This is a CLOSED BOOK/CLOSED NOTES exam. Select
More informationPossible logic functions of two variables
ombinational logic asic logic oolean algebra, proofs by re-writing, proofs by perfect induction logic functions, truth tables, and switches NOT, ND, OR, NND, NOR, OR,..., minimal set Logic realization
More informationMotivation for Lecture. For digital design we use CMOS transistors. Gate Source. CMOS symboler. MOS transistor. Depletion. A channel is created
Motivation for Lecture igital Integrated ircuits iktor Öwall o see how standard gates are implemented with transistors? How does technology affect the performance, e.g. speed and power consumption? What
More informationEE115C Digital Electronic Circuits Homework #4
EE115 Digital Electronic ircuits Homework #4 Problem 1 Power Dissipation Solution Vdd =1.0V onsider the source follower circuit used to drive a load L =20fF shown above. M1 and M2 are both NMOS transistors
More informationEE 447 VLSI Design. Lecture 5: Logical Effort
EE 447 VLSI Design Lecture 5: Logical Effort Outline Introduction Delay in a Logic Gate Multistage Logic Networks Choosing the Best Number of Stages Example Summary EE 4475: VLSI Logical Design Effort
More informationCARNEGIE MELLON UNIVERSITY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING DIGITAL INTEGRATED CIRCUITS FALL 2002
CARNEGIE MELLON UNIVERSITY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 18-322 DIGITAL INTEGRATED CIRCUITS FALL 2002 Final Examination, Monday Dec. 16, 2002 NAME: SECTION: Time: 180 minutes Closed
More informationEECS Variable Logic Functions
EECS150 Section 1 Introduction to Combinational Logic Fall 2001 2-Variable Logic Functions There are 16 possible functions of 2 input variables: in general, there are 2**(2**n) functions of n inputs X
More informationEE 434 Lecture 33. Logic Design
EE 434 Lecture 33 Logic Design Review from last time: Ask the inverter how it will interpret logic levels V IN V OUT V H =? V L =? V LARGE V H V L V H Review from last time: The two-inverter loop X Y X
More informationDigital- or Logic Circuits. Outline Logic Circuits. Logic Voltage Levels. Binary Representation
Outline Logic ircuits Introduction Logic Systems TTL MOS Logic Gates NOT, OR, N NOR, NN, XOR Implementation oolean lgebra ombinatorial ircuits Multipleer emultipleer rithmetic ircuits Simplifying Logic
More informationBoolean Algebra & Logic Gates. By : Ali Mustafa
Boolean Algebra & Logic Gates By : Ali Mustafa Digital Logic Gates There are three fundamental logical operations, from which all other functions, no matter how complex, can be derived. These Basic functions
More informationEE115C Digital Electronic Circuits Homework #5
EE115C Digital Electronic Circuits Homework #5 Due Thursday, May 13, 6pm @ 56-147E EIV Problem 1 Elmore Delay Analysis Calculate the Elmore delay from node A to node B using the values for the resistors
More informationLecture 7: Logic design. Combinational logic circuits
/24/28 Lecture 7: Logic design Binary digital circuits: Two voltage levels: and (ground and supply voltage) Built from transistors used as on/off switches Analog circuits not very suitable for generic
More informationContents. Chapter 3 Combinational Circuits Page 1 of 36
Chapter 3 Combinational Circuits Page of 36 Contents Combinational Circuits...2 3. Analysis of Combinational Circuits...3 3.. Using a Truth Table...3 3..2 Using a Boolean Function...6 3.2 Synthesis of
More informationComputer Science 324 Computer Architecture Mount Holyoke College Fall Topic Notes: Digital Logic
Computer Science 324 Computer Architecture Mount Holyoke College Fall 2007 Topic Notes: Digital Logic Our goal for the next few weeks is to paint a a reasonably complete picture of how we can go from transistor
More informationBOOLEAN ALGEBRA INTRODUCTION SUBSETS
BOOLEAN ALGEBRA M. Ragheb 1/294/2018 INTRODUCTION Modern algebra is centered around the concept of an algebraic system: A, consisting of a set of elements: ai, i=1, 2,, which are combined by a set of operations
More informationUNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences
UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences Elad Alon Homework #9 EECS141 PROBLEM 1: TIMING Consider the simple state machine shown
More informationCPE/EE 427, CPE 527 VLSI Design I L06: CMOS Inverter, CMOS Logic Gates. Course Administration. CMOS Inverter: A First Look
CPE/EE 47, CPE 57 VLSI esign I L6: CMOS Inverter, CMOS Logic Gates epartment of Electrical and Computer Engineering University of labama in Huntsville leksandar Milenkovic ( www.ece.uah.edu/~milenka )
More informationWorking with combinational logic
Working with combinational logic Simplification two-level simplification exploiting don t cares algorithm for simplification Logic realization two-level logic and canonical forms realized with NNs and
More informationCombinational logic systems
Combinational logic systems Learners should be able to: (a) recognise 1/0 as two-state logic levels (b) identify and use NOT gates and 2-input AND, OR, NAND and NOR gates, singly and in combination (c)
More informationUNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. Professor Oldham Fall 1999
UNIVERSITY OF CLIFORNI College of Engineering Department of Electrical Engineering and Computer Sciences Professor Oldham Fall 1999 EECS 40 FINL EXM 13 December 1999 Name: Last, First Student ID: T: Kusuma
More informationEE 330 Lecture 39. Digital Circuits. Propagation Delay basic characterization Device Sizing (Inverter and multiple-input gates)
EE 330 Lecture 39 Digital ircuits Propagation Delay basic characterization Device Sizing (Inverter and multiple-input gates) Review from last lecture Other MOS Logic Families Enhancement Load NMOS Enhancement
More informationElectrical Circuits. Winchester College Physics. makptb. c D. Common Time man. 3rd year Revision Test
Name... Set... Don.... manner~ man makptb Winchester College Physics 3rd year Revision Test Electrical Circuits Common Time 2011 Mark multiple choice answers with a cross (X) using the box below. I A B
More informationDigital Microelectronic Circuits ( ) Logical Effort. Lecture 7: Presented by: Adam Teman
Digital Microelectronic ircuits (361-1-3021 ) Presented by: Adam Teman Lecture 7: Logical Effort Digital Microelectronic ircuits The VLSI Systems enter - BGU Lecture 7: Logical Effort 1 Last Lectures The
More informationSlide Set 6. for ENEL 353 Fall Steve Norman, PhD, PEng. Electrical & Computer Engineering Schulich School of Engineering University of Calgary
Slide Set 6 for ENEL 353 Fall 2017 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary Fall Term, 2017 SN s ENEL 353 Fall 2017 Slide Set 6 slide
More informationCMOS Inverter: CPE/EE 427, CPE 527 VLSI Design I L06: CMOS Inverter, CMOS Logic Gates. Course Administration. CMOS Properties.
CMOS Inverter: Steady State Response CPE/EE 47, CPE 57 VLSI esign I L6: CMOS Inverter, CMOS Logic Gates R p V OL = V OH = V M = f(r n, R p ) epartment of Electrical and Computer Engineering University
More informationLecture 6: Logical Effort
Lecture 6: Logical Effort Outline Logical Effort Delay in a Logic Gate Multistage Logic Networks Choosing the Best Number of Stages Example Summary Introduction Chip designers face a bewildering array
More informationComputer Organization: Boolean Logic
Computer Organization: Boolean Logic Representing and Manipulating Data Last Unit How to represent data as a sequence of bits How to interpret bit representations Use of levels of abstraction in representing
More informationSimulation of Logic Primitives and Dynamic D-latch with Verilog-XL
Simulation of Logic Primitives and Dynamic D-latch with Verilog-XL November 30, 2011 Robert D Angelo Tufts University Electrical and Computer Engineering EE-103 Lab 3: Part I&II Professor: Dr. Valencia
More informationNAND, NOR and XOR functions properties
Laboratory NAND, NOR and XOR functions properties. Laboratory work goals Enumeration of NAND, NOR and XOR functions properties Presentation of NAND, NOR and XOR modules Realisation of circuits with gates
More informationCSE 140 Midterm I - Solution
CSE 140 Midterm I - Solution 1. Answer the following questions given the logic circuit below. (15 points) a. (5 points) How many CMOS transistors does the given (unsimplified) circuit have. b. (6 points)
More informationVery Large Scale Integration (VLSI)
Very Large Scale Integration (VLSI) Lecture 4 Dr. Ahmed H. Madian Ah_madian@hotmail.com Dr. Ahmed H. Madian-VLSI Contents Delay estimation Simple RC model Penfield-Rubenstein Model Logical effort Delay
More informationDigital Electronics. Part A
Digital Electronics Final Examination Part A Winter 2004-05 Student Name: Date: lass Period: Total Points: Multiple hoice Directions: Select the letter of the response which best completes the item or
More informationDigital Integrated Circuits A Design Perspective
Digital Integrated Circuits Design Perspective Jan M. Rabaey nantha Chandrakasan orivoje Nikolić Designing Combinational Logic Circuits November 2002. 1 Combinational vs. Sequential Logic In Combinational
More informationWeek-I. Combinational Logic & Circuits
Week-I Combinational Logic & Circuits Overview Binary logic operations and gates Switching algebra Algebraic Minimization Standard forms Karnaugh Map Minimization Other logic operators IC families and
More informationCircuits & Boolean algebra.
Circuits & Boolean algebra http://xkcd.com/730/ CSCI 255: Introduction to Embedded Systems Keith Vertanen Copyright 2011 Digital circuits Overview How a switch works Building basic gates from switches
More informationImplementation of Boolean Logic by Digital Circuits
Implementation of Boolean Logic by Digital Circuits We now consider the use of electronic circuits to implement Boolean functions and arithmetic functions that can be derived from these Boolean functions.
More informationIntroduction to Computer Engineering. CS/ECE 252, Fall 2012 Prof. Guri Sohi Computer Sciences Department University of Wisconsin Madison
Introduction to Computer Engineering CS/ECE 252, Fall 2012 Prof. Guri Sohi Computer Sciences Department University of Wisconsin Madison Chapter 3 Digital Logic Structures Slides based on set prepared by
More informationGates and Flip-Flops
Gates and Flip-Flops Chris Kervick (11355511) With Evan Sheridan and Tom Power December 2012 On a scale of 1 to 10, how likely is it that this question is using binary?...4? What s a 4? Abstract The operation
More informationCHAPTER 7 MULTI-LEVEL GATE CIRCUITS NAND AND NOR GATES
CHAPTER 7 MULTI-LEVEL GATE CIRCUITS NAND AND NOR GATES This chapter in the book includes: Objectives Study Guide 7.1 Multi-Level Gate Circuits 7.2 NAND and NOR Gates 7.3 Design of Two-Level Circuits Using
More informationMOS SWITCHING CIRCUITS
ontent MOS SWIHING IRUIS nmos Inverter nmos Logic Functions MOS Inverter UNBUFFR MOS LOGI BUFFR MOS LOGI A antoni 010igital Switching 1 MOS Inverters V V V V V R Pull Up Pu Pu Pu Pull own G B Pd Pd Pd
More informationVLSI Design I; A. Milenkovic 1
ourse dministration PE/EE 47, PE 57 VLI esign I L6: tatic MO Logic epartment of Electrical and omputer Engineering University of labama in Huntsville leksandar Milenkovic ( www. ece.uah.edu/~milenka )
More informationEECS 270 Midterm 2 Exam Answer Key Winter 2017
EES 270 Midterm 2 Exam nswer Key Winter 2017 Name: unique name: Sign the honor code: I have neither given nor received aid on this exam nor observed anyone else doing so. NOTES: 1. This part of the exam
More informationB.Supmonchai August 1st, q In-depth discussion of CMOS logic families. q Optimizing gate metrics. q High Performance circuit-design techniques
ugust st, 4 Goals of This hapter hapter 6 Static MOS ircuits oonchuay Supmonchai Integrated esign pplication Research (IR) Laboratory ugust, 4; Revised - June 8, 5 In-depth discussion of MOS logic families
More informationVLSI Design I; A. Milenkovic 1
ourse dministration PE/EE 47, PE 57 VLI esign I L6: omplementary MO Logic Gates epartment of Electrical and omputer Engineering University of labama in Huntsville leksandar Milenkovic ( www.ece.uah.edu/~milenka
More informationCS61c: Representations of Combinational Logic Circuits
CS61c: Representations of Combinational Logic Circuits J. Wawrzynek March 5, 2003 1 Introduction Recall that synchronous systems are composed of two basic types of circuits, combination logic circuits,
More informationVLSI Design I; A. Milenkovic 1
PE/EE 47, PE 57 VLI esign I L6: tatic MO Logic epartment of Electrical and omputer Engineering University of labama in Huntsville leksandar Milenkovic ( www. ece.uah.edu/~milenka ) www. ece.uah.edu/~milenka/cpe57-3f
More informationCMOS logic gates. João Canas Ferreira. March University of Porto Faculty of Engineering
CMOS logic gates João Canas Ferreira University of Porto Faculty of Engineering March 2016 Topics 1 General structure 2 General properties 3 Cell layout João Canas Ferreira (FEUP) CMOS logic gates March
More informationChapter 2: Boolean Algebra and Logic Gates
Chapter 2: Boolean Algebra and Logic Gates Mathematical methods that simplify binary logics or circuits rely primarily on Boolean algebra. Boolean algebra: a set of elements, a set of operators, and a
More informationCMOS Inverter. Performance Scaling
Announcements Exam #2 regrade requests due today. Homework #8 due today. Final Exam: Th June 12, 8:30 10:20am, CMU 120 (extension to 11:20am requested). Grades available for viewing via Catalyst. CMOS
More informationUnit 8A Computer Organization. Boolean Logic and Gates
Unit 8A Computer Organization Boolean Logic and Gates Announcements Bring ear buds or headphones to lab! 15110 Principles of Computing, Carnegie Mellon University - CORTINA 2 Representing and Manipulating
More informationCHAPTER * 6-2. a) 3-input NAND gate b) 4-input NOR gate * Pearson Education, Inc. a) F = (A + B) C D. b) G = (A + B) (C + D)
HPTER 6 6-.* a) = ( + ) b) G = ( + ) ( + ) 200 Pearson Education, Inc. 6-2. a) 3-input NN gate b) 4-input NOR gate +V +V 6-3. 6 inputs 6 inputs 6 inputs 6-4.* The longest path is from input or. 0.073 ns
More informationCMPEN 411. Spring Lecture 18: Static Sequential Circuits
CMPEN 411 VLSI Digital Circuits Spring 2011 Lecture 18: Static Sequential Circuits [Adapted from Rabaey s Digital Integrated Circuits, Second Edition, 2003 J. Rabaey, A. Chandrakasan, B. Nikolic] Sp11
More informationChapter 2 Combinational Logic Circuits
Logic and Computer Design Fundamentals Chapter 2 Combinational Logic Circuits Part 1 Gate Circuits and Boolean Equations Chapter 2 - Part 1 2 Chapter 2 - Part 1 3 Chapter 2 - Part 1 4 Chapter 2 - Part
More informationCombinational Logic. By : Ali Mustafa
Combinational Logic By : Ali Mustafa Contents Adder Subtractor Multiplier Comparator Decoder Encoder Multiplexer How to Analyze any combinational circuit like this? Analysis Procedure To obtain the output
More informationEE 466/586 VLSI Design. Partha Pande School of EECS Washington State University
EE 466/586 VLSI Design Partha Pande School of EECS Washington State University pande@eecs.wsu.edu Lecture 9 Propagation delay Power and delay Tradeoffs Follow board notes Propagation Delay Switching Time
More informationInterconnect (2) Buffering Techniques. Logical Effort
Interconnect (2) Buffering Techniques. Logical Effort Lecture 14 18-322 Fall 2002 Textbook: [Sections 4.2.1, 8.2.3] A few announcements! M1 is almost over: The check-off is due today (by 9:30PM) Students
More informationDesigning Information Devices and Systems II Spring 2016 Anant Sahai and Michel Maharbiz Homework 5. This homework is due February 29, 2016, at Noon.
EECS 16 Designing Information Devices and Systems II Spring 2016 nant Sahai and Michel Maharbiz Homework 5 This homework is due February 29, 2016, at Noon. 1. Homework process and study group Who else
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Sciences
MSSCHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Sciences nalysis and Design of Digital Integrated Circuits (6.374) - Fall 2003 Quiz #1 Prof. nantha Chandrakasan Student
More informationEE141-Fall 2011 Digital Integrated Circuits
EE4-Fall 20 Digital Integrated Circuits Lecture 5 Memory decoders Administrative Stuff Homework #6 due today Project posted Phase due next Friday Project done in pairs 2 Last Lecture Last lecture Logical
More information