Lecture 10: Combinational Circuits

Size: px
Start display at page:

Download "Lecture 10: Combinational Circuits"

Transcription

1 Computer Architecture Lecture : Combinational Circuits Previous two lectures.! TOY machine. Net two lectures.! Digital circuits. George Boole (85 864) Claude Shannon (96 2) Culminating lecture.! Putting it all together and building a TOY machine. COS26: General Computer Science 2 Digital Circuits Wires What is a digital sstem?! Digital: signals are or.! Analog: signals var continuousl. Wh digital sstems?! Accurac and reliabilit.! Staggeringl fast and cheap. Basic abstractions.! On, off.! Switch that can turn something on or off. Wires.! Propagate logical values from place to place.! Signals "flow" from left to right. A drawing convention, sometimes violated Actuall: flow from producer to consumer(s) of signal Digital circuits and ou.! Computer microprocessors.! Antilock brakes.! Cell phones. Input Output 3 4

2 Logic Gates Multiwa AND Gates Logical gates.! Fundamental building blocks. AND(,, 2, 3, 4, 5, 6, 7 ).! if all inputs are.! otherwise. ' NOT AND OR 5 6 Multiwa OR Gates Boolean Algebra OR(,, 2, 3, 4, 5, 6, 7 ).! if at least one input is.! otherwise. Histor.! Developed b Boole to solve mathematical logic problems (847).! Shannon first applied to digital circuits (937). Basics.! Boolean variable: value is or.! Boolean function: function whose inputs and outputs are,. Relationship to circuits.! Boolean variables: signals.! Boolean functions: circuits. 7 8

3 Truth Table Truth Table for Functions of 2 Variables Truth table.! Sstematic method to describe Boolean function.! One row for each possible input combination.! N inputs! 2 N rows. Truth table.! 6 Boolean functions of 2 variables. ever 4-bit value represents one Truth Table for All Boolean Functions of 2 Variables AND Truth Table AND(, ) ZERO AND XOR Truth Table for All Boolean Functions of 2 Variables NOR EQ ' ' NAND OR ONE AND 9 Truth Table for Functions of 3 Variables Universalit of AND, OR, NOT Truth table.! 6 Boolean functions of 2 variables. ever 4-bit value represents one! 256 Boolean functions of 3 variables. ever 8-bit value represents one! 2^(2^N) Boolean functions of N variables! Some Functions of 3 Variables z AND OR MAJ ODD An Boolean function can be epressed using AND, OR, NOT.! "Universal."! XOR(,) = ' ' Epressing XOR Using AND, OR, NOT ' ' ' ' ' ' XOR Notation ' Eercise: {AND, NOT}, {OR, NOT}, {NAND}, {AND, XOR} are universal. Meaning NOT AND OR 2

4 Sum-of-Products Translate Boolean Formula to Boolean Circuit An Boolean function can be epressed using AND, OR, NOT.! Sum-of-products is sstematic procedure. form AND term for each in truth table of Boolean function OR terms together Use sum-of-products form.! XOR(, ) = ' '. Epressing MAJ Using Sum-of-Products z MAJ 'z 'z z' z 'z 'z z' z 3 4 Translate Boolean Formula to Boolean Circuit Simplification Using Boolean Algebra Use sum-of-products form.! MAJ(,, z) = 'z 'z z' z. Man possible circuits for each Boolean function.! Sum-of-products not necessaril optimal in: number of gates (space) depth of circuit (time)! MAJ(,, z) = 'z 'z z' z = z z. size = 8, depth = 3 size = 4, depth = 2 5 6

5 Epressing a Boolean Function Using AND, OR, NOT ODD Parit Circuit Ingredients.! AND gates.! OR gates.! NOT gates.! Wire. ODD(,, z).! if odd number of inputs are.! otherwise. Epressing ODD Using Sum-of-Products Instructions.! Step : represent input and output signals with Boolean variables.! Step 2: construct truth table to carr out computation.! Step 3: derive (simplified) Boolean epression using sum-of products.! Step 4: transform Boolean epression into circuit. z ODD ''z 'z' 'z' z ''z 'z' 'z' z 7 8 ODD Parit Circuit Let's Make an Adder Circuit ODD(,, z).! if odd number of inputs are.! otherwise. Goal: = z for 4-bit integers.! We build 4-bit adder: 9 inputs, 4 outputs.! Same idea scales to 28-bit adder.! Ke computer component Step.! Represent input and output in binar c z 3 z 2 z z z 3 z 2 z z 9 2

6 Let's Make an Adder Circuit Let's Make an Adder Circuit Goal: = z for 4-bit integers. c Goal: = z for 4-bit integers. c 3 c = c 2 c Step 2. (first attempt)! Build truth table. 3 2 Step 2. (do one bit at a time)! Build truth table for carr bit. 3 2! Wh is this a bad idea? z 3 z 2 z z! Build truth table for summand bit. z 3 z 2 z z 28-bit adder: rows > # electrons in universe! c Bit Adder Truth Table 3 2 z 3 z 2 z z 2 8 = 52 rows! Carr Bit i i c i c i Summand Bit i i c i z i 2 22 Let's Make an Adder Circuit Let's Make an Adder Circuit Goal: = z for 4-bit integers. c 3 c = c 2 c Goal: = z for 4-bit integers. 3 2 Step 3.! Derive (simplified) Boolean epression. 3 2 Step 4.! Transform Boolean epression into circuit. z 3 z 2 z z! Chain together -bit adders. Carr Bit Summand Bit i i c i c i MAJ i i c i z i ODD 23 24

7 Let's Make an Adder Circuit Subtractor Goal: = z for 4-bit integers. Step 4.! Transform Boolean epression into circuit.! Chain together -bit adders. Subtractor circuit: z = -.! One approach: design like adder circuit.! Better idea: reuse adder circuit. 2's complement: to negate an integer, flip bits, then add carr z 3 z 2 z z 4-Bit Subtractor Interface 4-Bit Subtractor Implementation Arithmetic Logic Unit: Interface Arithmetic Logic Unit: Implementation ALU Interface.! Add, subtract, bitwise and, bitwise or, shift left, shift right, cop.! Associate 3-bit integer with 5 primar ALU operations. ALU performs operations in parallel control wires select which result ALU outputs Input Input ~ carr in op 2, - & ^ <<, >> input 2 Input Input shift direction ALU subtract 3 ALU select 6 27 op 2, - & ^ <<, >> input 2 subtract & ^^ << >> shift direction MUX 3 ALU control 6 28

8 Summar Lessons for software design appl to hardware design!! Interface describes behavior of circuit.! Implementation gives details of how to build it. Laers of abstraction appl with a vengeance!! On/off.! Controlled switch (transistor).! Gates (AND, OR, NOT).! Boolean circuit (MAJ, ODD).! Adder.!.! Arithmetic logic unit.!.! TOY machine. 29

6: Combinational Circuits

6: Combinational Circuits Computer Architecture 6: Combinational Circuits Previous two lectures. von Neumann machine. This lectures. Boolean circuits. Later in the course. Putting it all together and building a TOY machine. George

More information

6.1 Combinational Circuits. George Boole ( ) Claude Shannon ( )

6.1 Combinational Circuits. George Boole ( ) Claude Shannon ( ) 6. Combinational Circuits George Boole (85 864) Claude Shannon (96 2) Digital signals Binary (or logical ) values: or, on or off, high or low voltage Wires. Propagate logical values from place to place.

More information

6. Combinational Circuits. Building Blocks. Digital Circuits. Wires. Q. What is a digital system? A. Digital: signals are 0 or 1.

6. Combinational Circuits. Building Blocks. Digital Circuits. Wires. Q. What is a digital system? A. Digital: signals are 0 or 1. Digital Circuits 6 Combinational Circuits Q What is a digital system? A Digital: signals are or analog: signals vary continuously Q Why digital systems? A Accurate, reliable, fast, cheap Basic abstractions

More information

Combinational Circuits

Combinational Circuits Combinational Circuits Q. What is a combinational circuit? A. Digital: signals are or. A. No feedback: no loops. analog circuits: signals vary continuously sequential circuits: loops allowed (stay tuned)

More information

6.1 Combinational Circuits. George Boole ( ) Claude Shannon ( )

6.1 Combinational Circuits. George Boole ( ) Claude Shannon ( ) 6. Combinational Circuits George Boole (85 864) Claude Shannon (96 2) Signals and Wires Digital signals Binary (or logical ) values: or, on or off, high or low voltage Wires. Propagate digital signals

More information

Arithmetic Logic Unit (ALU)

Arithmetic Logic Unit (ALU) Arithmetic Logic Unit (ALU) Introduction to Computer Yung-Yu Chuang with slides by Sedgewick & Wayne (introcs.cs.princeton.edu), Nisan & Schocken (www.nand2tetris.org) and Harris & Harris (DDCA) Let's

More information

Combinational Circuits Digital Logic (Materials taken primarily from:

Combinational Circuits Digital Logic (Materials taken primarily from: Combinational Circuits Digital Logic (Materials taken primarily from: http://www.facstaff.bucknell.edu/mastascu/elessonshtml/eeindex.html http://www.cs.princeton.edu/~cos126 ) Digital Systems What is a

More information

ECEN 468 Advanced Logic Design

ECEN 468 Advanced Logic Design ECEN 468 Advanced Logic Design Lecture 26: Verilog Operators ECEN 468 Lecture 26 Operators Operator Number of Operands Result Arithmetic 2 Binary word Bitwise 2 Binary word Reduction 1 Bit Logical 2 Boolean

More information

Parallel logic circuits

Parallel logic circuits Computer Mathematics Week 9 Parallel logic circuits College of Information cience and Engineering Ritsumeikan University last week the mathematics of logic circuits the foundation of all digital design

More information

Software and Hardware

Software and Hardware Software and Hardware Numbers At the most fundamental level, a computer manipulates electricity according to specific rules To make those rules produce something useful, we need to associate the electrical

More information

Computer Organization and Levels of Abstraction

Computer Organization and Levels of Abstraction Computer Organization and Levels of Abstraction Announcements Today: PS 7 Lab 8: Sound Lab tonight bring machines and headphones! PA 7 Tomorrow: Lab 9 Friday: PS8 Today (Short) Floating point review Boolean

More information

BUILDING BLOCKS OF A BASIC MICROPROCESSOR. Part 1 PowerPoint Format of Lecture 3 of Book

BUILDING BLOCKS OF A BASIC MICROPROCESSOR. Part 1 PowerPoint Format of Lecture 3 of Book BUILDING BLOCKS OF A BASIC MICROPROCESSOR Part PowerPoint Format of Lecture 3 of Book Decoder Tri-state device Full adder, full subtractor Arithmetic Logic Unit (ALU) Memories Example showing how to write

More information

Binary Adders: Half Adders and Full Adders

Binary Adders: Half Adders and Full Adders Binary Adders: Half Adders and Full Adders In this set of slides, we present the two basic types of adders: 1. Half adders, and 2. Full adders. Each type of adder functions to add two binary bits. In order

More information

Introduction to Boole algebra. Binary algebra

Introduction to Boole algebra. Binary algebra Introduction to Boole algebra Binary algebra Boole algebra George Boole s book released in 1847 We have only two digits: true and false We have NOT, AND, OR, XOR etc operations We have axioms and theorems

More information

QUESTION BANK FOR TEST

QUESTION BANK FOR TEST CSCI 2121 Computer Organization and Assembly Language PRACTICE QUESTION BANK FOR TEST 1 Note: This represents a sample set. Please study all the topics from the lecture notes. Question 1. Multiple Choice

More information

Arithmetic-logic units

Arithmetic-logic units Arithmetic-logic units An arithmetic-logic unit, or ALU, performs many different arithmetic and logic operations. The ALU is the heart of a processor you could say that everything else in the CPU is there

More information

Computer Organization and Levels of Abstraction

Computer Organization and Levels of Abstraction Computer Organization and Levels of Abstraction Announcements PS8 Due today PS9 Due July 22 Sound Lab tonight bring machines and headphones! Binary Search Today Review of binary floating point notation

More information

24 Nov Boolean Operations. Boolean Algebra. Boolean Functions and Expressions. Boolean Functions and Expressions

24 Nov Boolean Operations. Boolean Algebra. Boolean Functions and Expressions. Boolean Functions and Expressions 24 Nov 25 Boolean Algebra Boolean algebra provides the operations and the rules for working with the set {, }. These are the rules that underlie electronic circuits, and the methods we will discuss are

More information

UC Berkeley College of Engineering, EECS Department CS61C: Combinational Logic Blocks

UC Berkeley College of Engineering, EECS Department CS61C: Combinational Logic Blocks 2 Wawrzynek, Garcia 2004 c UCB UC Berkeley College of Engineering, EECS Department CS61C: Combinational Logic Blocks 1 Introduction Original document by J. Wawrzynek (2003-11-15) Revised by Chris Sears

More information

UC Berkeley College of Engineering, EECS Department CS61C: Combinational Logic Blocks

UC Berkeley College of Engineering, EECS Department CS61C: Combinational Logic Blocks UC Berkeley College of Engineering, EECS Department CS61C: Combinational Logic Blocks Original document by J. Wawrzynek (2003-11-15) Revised by Chris Sears and Dan Garcia (2004-04-26) 1 Introduction Last

More information

Department of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering Assignment 2 Combinational Logic

Department of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering Assignment 2 Combinational Logic Department of Electrical Engineering McGill University ECSE 221 Introduction to Computer Engineering Assignment 2 Combinational Logic Question 1: Due October 19 th, 2009 A convenient shorthand for specifying

More information

CSC 220: Computer Organization Unit 10 Arithmetic-logic units

CSC 220: Computer Organization Unit 10 Arithmetic-logic units College of Computer and Information Sciences Department of Computer Science CSC 220: Computer Organization Unit 10 Arithmetic-logic units 1 Remember: 2 Arithmetic-logic units An arithmetic-logic unit,

More information

Von Neumann Architecture

Von Neumann Architecture Von Neumann Architecture Assist lecturer Donya A. Khalid Lecture 2 2/29/27 Computer Organization Introduction In 945, just after the World War, Jon Von Neumann proposed to build a more flexible computer.

More information

Basic Arithmetic (adding and subtracting)

Basic Arithmetic (adding and subtracting) Basic Arithmetic (adding and subtracting) Digital logic to show add/subtract Boolean algebra abstraction of physical, analog circuit behavior 1 0 CPU components ALU logic circuits logic gates transistors

More information

Register Transfer Language and Microoperations (Part 2)

Register Transfer Language and Microoperations (Part 2) Register Transfer Language and Microoperations (Part 2) Adapted by Dr. Adel Ammar Computer Organization 1 MICROOPERATIONS Computer system microoperations are of four types: Register transfer microoperations

More information

Gate-Level Minimization. section instructor: Ufuk Çelikcan

Gate-Level Minimization. section instructor: Ufuk Çelikcan Gate-Level Minimization section instructor: Ufuk Çelikcan Compleity of Digital Circuits Directly related to the compleity of the algebraic epression we use to build the circuit. Truth table may lead to

More information

Chapter 4 Arithmetic Functions

Chapter 4 Arithmetic Functions Logic and Computer Design Fundamentals Chapter 4 Arithmetic Functions Charles Kime & Thomas Kaminski 2008 Pearson Education, Inc. (Hyperlinks are active in View Show mode) Overview Iterative combinational

More information

Lecture (04) Boolean Algebra and Logic Gates

Lecture (04) Boolean Algebra and Logic Gates Lecture (4) Boolean Algebra and Logic Gates By: Dr. Ahmed ElShafee ١ Dr. Ahmed ElShafee, ACU : Spring 26, Logic Design Boolean algebra properties basic assumptions and properties: Closure law A set S is

More information

Lecture (04) Boolean Algebra and Logic Gates By: Dr. Ahmed ElShafee

Lecture (04) Boolean Algebra and Logic Gates By: Dr. Ahmed ElShafee Lecture (4) Boolean Algebra and Logic Gates By: Dr. Ahmed ElShafee Boolean algebra properties basic assumptions and properties: Closure law A set S is closed with respect to a binary operator, for every

More information

ECE 341 Midterm Exam

ECE 341 Midterm Exam ECE 341 Midterm Exam Time allowed: 75 minutes Total Points: 75 Points Scored: Name: Problem No. 1 (8 points) For each of the following statements, indicate whether the statement is TRUE or FALSE: (a) A

More information

Lecture Topics. Announcements. Today: Integer Arithmetic (P&H ) Next: continued. Consulting hours. Introduction to Sim. Milestone #1 (due 1/26)

Lecture Topics. Announcements. Today: Integer Arithmetic (P&H ) Next: continued. Consulting hours. Introduction to Sim. Milestone #1 (due 1/26) Lecture Topics Today: Integer Arithmetic (P&H 3.1-3.4) Next: continued 1 Announcements Consulting hours Introduction to Sim Milestone #1 (due 1/26) 2 1 Overview: Integer Operations Internal representation

More information

Henry Lin, Department of Electrical and Computer Engineering, California State University, Bakersfield Lecture 7 (Digital Logic) July 24 th, 2012

Henry Lin, Department of Electrical and Computer Engineering, California State University, Bakersfield Lecture 7 (Digital Logic) July 24 th, 2012 Henry Lin, Department of Electrical and Computer Engineering, California State University, Bakersfield Lecture 7 (Digital Logic) July 24 th, 2012 1 Digital vs Analog Digital signals are binary; analog

More information

REGISTER TRANSFER AND MICROOPERATIONS

REGISTER TRANSFER AND MICROOPERATIONS REGISTER TRANSFER AND MICROOPERATIONS Register Transfer Language Register Transfer Bus and Memory Transfers Arithmetic Microoperations Logic Microoperations Shift Microoperations Arithmetic Logic Shift

More information

REGISTER TRANSFER AND MICROOPERATIONS

REGISTER TRANSFER AND MICROOPERATIONS 1 REGISTER TRANSFER AND MICROOPERATIONS Register Transfer Language Register Transfer Bus and Memory Transfers Arithmetic Microoperations Logic Microoperations Shift Microoperations Arithmetic Logic Shift

More information

ECE 2030B 1:00pm Computer Engineering Spring problems, 5 pages Exam Two 10 March 2010

ECE 2030B 1:00pm Computer Engineering Spring problems, 5 pages Exam Two 10 March 2010 Instructions: This is a closed book, closed note exam. Calculators are not permitted. If you have a question, raise your hand and I will come to you. Please work the exam in pencil and do not separate

More information

Boolean Functions (10.1) Representing Boolean Functions (10.2) Logic Gates (10.3)

Boolean Functions (10.1) Representing Boolean Functions (10.2) Logic Gates (10.3) Chapter (Part ): Boolean Algebra Boolean Functions (.) Representing Boolean Functions (.2) Logic Gates (.3) It has started from the book titled The laws of thought written b George Boole in 854 Claude

More information

Electronic Engineering Part 1 Laboratory Experiment. Digital Circuit Design 1 Combinational Logic. (3 hours)

Electronic Engineering Part 1 Laboratory Experiment. Digital Circuit Design 1 Combinational Logic. (3 hours) Electronic Engineering Part 1 Laboratory Experiment Digital Circuit Design 1 Combinational Logic (3 hours) 1. Introduction These days most signal processing is done digitally. Electronic signals (representing

More information

Digital Logic Design Exercises. Assignment 1

Digital Logic Design Exercises. Assignment 1 Assignment 1 For Exercises 1-5, match the following numbers with their definition A Number Natural number C Integer number D Negative number E Rational number 1 A unit of an abstract mathematical system

More information

Combinational and sequential circuits (learned in Chapters 1 and 2) can be used to create simple digital systems.

Combinational and sequential circuits (learned in Chapters 1 and 2) can be used to create simple digital systems. REGISTER TRANSFER AND MICROOPERATIONS Register Transfer Language Register Transfer Bus and Memory Transfers Arithmetic Microoperations Logic Microoperations Shift Microoperations Arithmetic Logic Shift

More information

ENGIN 112. Intro to Electrical and Computer Engineering

ENGIN 112. Intro to Electrical and Computer Engineering ENIN 2 Intro to Electrical and Computer Engineering Lecture 6 More Boolean Algebra ENIN2 L6: More Boolean Algebra September 5, 23 A B Overview Epressing Boolean functions Relationships between algebraic

More information

END-TERM EXAMINATION

END-TERM EXAMINATION (Please Write your Exam Roll No. immediately) END-TERM EXAMINATION DECEMBER 2006 Exam. Roll No... Exam Series code: 100919DEC06200963 Paper Code: MCA-103 Subject: Digital Electronics Time: 3 Hours Maximum

More information

UNIT II - COMBINATIONAL LOGIC Part A 2 Marks. 1. Define Combinational circuit A combinational circuit consist of logic gates whose outputs at anytime are determined directly from the present combination

More information

Review. Pipeline big-delay CL for faster clock Finite State Machines extremely useful You ll see them again in 150, 152 & 164

Review. Pipeline big-delay CL for faster clock Finite State Machines extremely useful You ll see them again in 150, 152 & 164 CS61C L17 Combinatorial Logic Blocks (1) inst.eecs.berkeley.edu/~cs61c CS61C : Machine Structures Lecture #17 Combinatorial Logic Blocks 2007-7-24 Scott Beamer, Instructor Review Pipeline big-delay CL

More information

CS 261 Fall Mike Lam, Professor. Combinational Circuits

CS 261 Fall Mike Lam, Professor. Combinational Circuits CS 261 Fall 2017 Mike Lam, Professor Combinational Circuits The final frontier Java programs running on Java VM C programs compiled on Linux Assembly / machine code on CPU + memory??? Switches and electric

More information

REGISTER TRANSFER LANGUAGE

REGISTER TRANSFER LANGUAGE REGISTER TRANSFER LANGUAGE The operations executed on the data stored in the registers are called micro operations. Classifications of micro operations Register transfer micro operations Arithmetic micro

More information

1. Prove that if you have tri-state buffers and inverters, you can build any combinational logic circuit. [4]

1. Prove that if you have tri-state buffers and inverters, you can build any combinational logic circuit. [4] HW 3 Answer Key 1. Prove that if you have tri-state buffers and inverters, you can build any combinational logic circuit. [4] You can build a NAND gate from tri-state buffers and inverters and thus you

More information

DIGITAL ELECTRONICS. P41l 3 HOURS

DIGITAL ELECTRONICS. P41l 3 HOURS UNIVERSITY OF SWAZILAND FACUL TY OF SCIENCE AND ENGINEERING DEPARTMENT OF PHYSICS MAIN EXAMINATION 2015/16 TITLE OF PAPER: COURSE NUMBER: TIME ALLOWED: INSTRUCTIONS: DIGITAL ELECTRONICS P41l 3 HOURS ANSWER

More information

ECE 2030D Computer Engineering Spring problems, 5 pages Exam Two 8 March 2012

ECE 2030D Computer Engineering Spring problems, 5 pages Exam Two 8 March 2012 Instructions: This is a closed book, closed note exam. Calculators are not permitted. If you have a question, raise your hand and I will come to you. Please work the exam in pencil and do not separate

More information

CS61C : Machine Structures

CS61C : Machine Structures inst.eecs.berkeley.edu/~cs61c/su06 CS61C : Machine Structures Lecture #14: Combinational Logic, Gates, and State 2006-07-20 CS 61C L14 Combinational Logic (1) Andy Carle What are Machine Structures? Software

More information

CARLETON UNIVERSITY. Laboratory 2.0

CARLETON UNIVERSITY. Laboratory 2.0 CARLETON UNIVERSITY Department of Electronics ELEC 267 Switching Circuits Jan 3, 28 Overview Laboratory 2. A 3-Bit Binary Sign-Extended Adder/Subtracter A binary adder sums two binary numbers for example

More information

Solutions - Homework 2 (Due date: February 5 5:30 pm) Presentation and clarity are very important! Show your procedure!

Solutions - Homework 2 (Due date: February 5 5:30 pm) Presentation and clarity are very important! Show your procedure! Solutions - Homework (Due date: Februar 5 th @ 5: pm) Presentation and clarit are ver important! Show our procedure! PROBLEM ( PTS) In these problems, ou MUST show our conversion procedure. a) Convert

More information

ECE 550D Fundamentals of Computer Systems and Engineering. Fall 2017

ECE 550D Fundamentals of Computer Systems and Engineering. Fall 2017 ECE 550D Fundamentals of Computer Systems and Engineering Fall 2017 Combinational Logic Prof. John Board Duke University Slides are derived from work by Profs. Tyler Bletsch and Andrew Hilton (Duke) Last

More information

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING, THE UNIVERSITY OF NEW MEXICO ECE-238L: Computer Logic Design Fall 2013.

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING, THE UNIVERSITY OF NEW MEXICO ECE-238L: Computer Logic Design Fall 2013. ECE-8L: Computer Logic Design Fall Notes - Chapter BINARY NUMBER CONVERSIONS DECIMAL NUMBER SYSTEM A decimal digit can take values from to 9: Digit-b-digit representation of a positive integer number (powers

More information

Computer Architecture and Organization: L04: Micro-operations

Computer Architecture and Organization: L04: Micro-operations Computer Architecture and Organization: L4: Micro-operations By: A. H. Abdul Hafez Abdul.hafez@hku.edu.tr, ah.abdulhafez@gmail.com, hafez@research.iiit.ac.in 1 Outlines 1. Arithmetic microoperation 2.

More information

Experiment 7 Arithmetic Circuits Design and Implementation

Experiment 7 Arithmetic Circuits Design and Implementation Experiment 7 Arithmetic Circuits Design and Implementation Introduction: Addition is just what you would expect in computers. Digits are added bit by bit from right to left, with carries passed to the

More information

CS/COE 0447 Example Problems for Exam 2 Spring 2011

CS/COE 0447 Example Problems for Exam 2 Spring 2011 CS/COE 0447 Example Problems for Exam 2 Spring 2011 1) Show the steps to multiply the 4-bit numbers 3 and 5 with the fast shift-add multipler. Use the table below. List the multiplicand (M) and product

More information

Topics. Computer Organization CS Exam 2 Review. Infix Notation. Reverse Polish Notation (RPN)

Topics. Computer Organization CS Exam 2 Review. Infix Notation. Reverse Polish Notation (RPN) Computer Organization CS 231-01 Exam 2 Review Dr. William H. Robinson October 11, 2004 http://eecs.vanderbilt.edu/courses/cs231/ Topics Education is a progressive discovery of our own ignorance. Will Durant

More information

Gate-Level Minimization. BME208 Logic Circuits Yalçın İŞLER

Gate-Level Minimization. BME208 Logic Circuits Yalçın İŞLER Gate-Level Minimization BME28 Logic Circuits Yalçın İŞLER islerya@yahoo.com http://me.islerya.com Complexity of Digital Circuits Directly related to the complexity of the algebraic expression we use to

More information

CHAPTER 4: Register Transfer Language and Microoperations

CHAPTER 4: Register Transfer Language and Microoperations CS 224: Computer Organization S.KHABET CHAPTER 4: Register Transfer Language and Microoperations Outline Register Transfer Language Register Transfer Bus and Memory Transfers Arithmetic Microoperations

More information

Review. Steps to writing (stateless) circuits: Create a logic function (one per output)

Review. Steps to writing (stateless) circuits: Create a logic function (one per output) MIPS ALU Review Steps to writing (stateless) circuits: Create a truth table Go through all different combinations of inputs For each row, generate each output based on the problem description Create a

More information

EE292: Fundamentals of ECE

EE292: Fundamentals of ECE EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 22 121115 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review Binary Number Representation Binary Arithmetic Combinatorial Logic

More information

4. Write a sum-of-products representation of the following circuit. Y = (A + B + C) (A + B + C)

4. Write a sum-of-products representation of the following circuit. Y = (A + B + C) (A + B + C) COP 273, Winter 26 Exercises 2 - combinational logic Questions. How many boolean functions can be defined on n input variables? 2. Consider the function: Y = (A B) (A C) B (a) Draw a combinational logic

More information

Combinational Logic II

Combinational Logic II Combinational Logic II Ranga Rodrigo July 26, 2009 1 Binary Adder-Subtractor Digital computers perform variety of information processing tasks. Among the functions encountered are the various arithmetic

More information

1 /10 2 /12 3 /16 4 /30 5 /12 6 /20

1 /10 2 /12 3 /16 4 /30 5 /12 6 /20 M A S S A C H U S E T T S I N S T I T U T E O F T E C H N O L O G Y DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE 6.004 Computation Structures Fall 2018 Practice Quiz #1 1 /10 2 /12 3 /16 4

More information

CS 31: Intro to Systems Digital Logic. Kevin Webb Swarthmore College February 2, 2016

CS 31: Intro to Systems Digital Logic. Kevin Webb Swarthmore College February 2, 2016 CS 31: Intro to Systems Digital Logic Kevin Webb Swarthmore College February 2, 2016 Reading Quiz Today Hardware basics Machine memory models Digital signals Logic gates Circuits: Borrow some paper if

More information

EXPERIMENT #8: BINARY ARITHMETIC OPERATIONS

EXPERIMENT #8: BINARY ARITHMETIC OPERATIONS EE 2 Lab Manual, EE Department, KFUPM EXPERIMENT #8: BINARY ARITHMETIC OPERATIONS OBJECTIVES: Design and implement a circuit that performs basic binary arithmetic operations such as addition, subtraction,

More information

Lecture #21 March 31, 2004 Introduction to Gates and Circuits

Lecture #21 March 31, 2004 Introduction to Gates and Circuits Lecture #21 March 31, 2004 Introduction to Gates and Circuits To this point we have looked at computers strictly from the perspective of assembly language programming. While it is possible to go a great

More information

DLD VIDYA SAGAR P. potharajuvidyasagar.wordpress.com. Vignana Bharathi Institute of Technology UNIT 3 DLD P VIDYA SAGAR

DLD VIDYA SAGAR P. potharajuvidyasagar.wordpress.com. Vignana Bharathi Institute of Technology UNIT 3 DLD P VIDYA SAGAR DLD UNIT III Combinational Circuits (CC), Analysis procedure, Design Procedure, Combinational circuit for different code converters and other problems, Binary Adder- Subtractor, Decimal Adder, Binary Multiplier,

More information

UNIT - V MEMORY P.VIDYA SAGAR ( ASSOCIATE PROFESSOR) Department of Electronics and Communication Engineering, VBIT

UNIT - V MEMORY P.VIDYA SAGAR ( ASSOCIATE PROFESSOR) Department of Electronics and Communication Engineering, VBIT UNIT - V MEMORY P.VIDYA SAGAR ( ASSOCIATE PROFESSOR) contents Memory: Introduction, Random-Access memory, Memory decoding, ROM, Programmable Logic Array, Programmable Array Logic, Sequential programmable

More information

Chapter 3 Arithmetic for Computers

Chapter 3 Arithmetic for Computers Chapter 3 Arithmetic for Computers 1 Arithmetic Where we've been: Abstractions: Instruction Set Architecture Assembly Language and Machine Language What's up ahead: Implementing the Architecture operation

More information

Chapter 4. Combinational Logic

Chapter 4. Combinational Logic Chapter 4. Combinational Logic Tong In Oh 1 4.1 Introduction Combinational logic: Logic gates Output determined from only the present combination of inputs Specified by a set of Boolean functions Sequential

More information

1. Mark the correct statement(s)

1. Mark the correct statement(s) 1. Mark the correct statement(s) 1.1 A theorem in Boolean algebra: a) Can easily be proved by e.g. logic induction b) Is a logical statement that is assumed to be true, c) Can be contradicted by another

More information

Boolean logic. Boolean Algebra. Introduction to Computer Yung-Yu Chuang NOT AND NOT

Boolean logic. Boolean Algebra. Introduction to Computer Yung-Yu Chuang NOT AND NOT oolean lgebra oolean logic ased on symbolic logic, designed by George oole oolean variables take values as or. oolean expressions created from: NOT, ND, OR Introduction to Computer ung-u Chuang with slides

More information

Combinational Circuits

Combinational Circuits Combinational Circuits Jason Filippou CMSC250 @ UMCP 06-02-2016 ason Filippou (CMSC250 @ UMCP) Circuits 06-02-2016 1 / 1 Outline ason Filippou (CMSC250 @ UMCP) Circuits 06-02-2016 2 / 1 Hardware design

More information

Lecture (03) Binary Codes Registers and Logic Gates

Lecture (03) Binary Codes Registers and Logic Gates Lecture (03) Binary Codes Registers and Logic Gates By: Dr. Ahmed ElShafee Binary Codes Digital systems use signals that have two distinct values and circuit elements that have two stable states. binary

More information

COMP combinational logic 1 Jan. 18, 2016

COMP combinational logic 1 Jan. 18, 2016 In lectures 1 and 2, we looked at representations of numbers. For the case of integers, we saw that we could perform addition of two numbers using a binary representation and using the same algorithm that

More information

Arithmetic Circuits. Design of Digital Circuits 2014 Srdjan Capkun Frank K. Gürkaynak.

Arithmetic Circuits. Design of Digital Circuits 2014 Srdjan Capkun Frank K. Gürkaynak. Arithmetic Circuits Design of Digital Circuits 2014 Srdjan Capkun Frank K. Gürkaynak http://www.syssec.ethz.ch/education/digitaltechnik_14 Adapted from Digital Design and Computer Architecture, David Money

More information

Basic operators, Arithmetic, Relational, Bitwise, Logical, Assignment, Conditional operators. JAVA Standard Edition

Basic operators, Arithmetic, Relational, Bitwise, Logical, Assignment, Conditional operators. JAVA Standard Edition Basic operators, Arithmetic, Relational, Bitwise, Logical, Assignment, Conditional operators JAVA Standard Edition Java - Basic Operators Java provides a rich set of operators to manipulate variables.

More information

COMPUTER ARCHITECTURE AND ORGANIZATION Register Transfer and Micro-operations 1. Introduction A digital system is an interconnection of digital

COMPUTER ARCHITECTURE AND ORGANIZATION Register Transfer and Micro-operations 1. Introduction A digital system is an interconnection of digital Register Transfer and Micro-operations 1. Introduction A digital system is an interconnection of digital hardware modules that accomplish a specific information-processing task. Digital systems vary in

More information

UPY14602-DIGITAL ELECTRONICS AND MICROPROCESSORS Lesson Plan

UPY14602-DIGITAL ELECTRONICS AND MICROPROCESSORS Lesson Plan UPY14602-DIGITAL ELECTRONICS AND MICROPROCESSORS Lesson Plan UNIT I - NUMBER SYSTEMS AND LOGIC GATES Introduction to decimal- Binary- Octal- Hexadecimal number systems-inter conversions-bcd code- Excess

More information

CS 31: Intro to Systems Digital Logic. Kevin Webb Swarthmore College February 3, 2015

CS 31: Intro to Systems Digital Logic. Kevin Webb Swarthmore College February 3, 2015 CS 31: Intro to Systems Digital Logic Kevin Webb Swarthmore College February 3, 2015 Reading Quiz Today Hardware basics Machine memory models Digital signals Logic gates Circuits: Borrow some paper if

More information

Propositional Calculus. Math Foundations of Computer Science

Propositional Calculus. Math Foundations of Computer Science Propositional Calculus Math Foundations of Computer Science Propositional Calculus Objective: To provide students with the concepts and techniques from propositional calculus so that they can use it to

More information

Mark Redekopp, All rights reserved. EE 352 Unit 8. HW Constructs

Mark Redekopp, All rights reserved. EE 352 Unit 8. HW Constructs EE 352 Unit 8 HW Constructs Logic Circuits Combinational logic Perform a specific function (mapping of 2 n input combinations to desired output combinations) No internal state or feedback Given a set of

More information

20 Calculus and Structures

20 Calculus and Structures 0 Calculus and Structures CHAPTER FUNCTIONS Calculus and Structures Copright LESSON FUNCTIONS. FUNCTIONS A function f is a relationship between an input and an output and a set of instructions as to how

More information

5. Minimizing Circuits

5. Minimizing Circuits 5. MINIMIZING CIRCUITS 46 5. Minimizing Circuits 5.. Minimizing Circuits. A circuit is minimized if it is a sum-of-products that uses the least number of products of literals and each product contains

More information

II/IV B.Tech (Regular/Supplementary) DEGREE EXAMINATION. Answer ONE question from each unit.

II/IV B.Tech (Regular/Supplementary) DEGREE EXAMINATION. Answer ONE question from each unit. Hall Ticket Number: 14CS IT303 November, 2017 Third Semester Time: Three Hours Answer Question No.1 compulsorily. II/IV B.Tech (Regular/Supplementary) DEGREE EXAMINATION Common for CSE & IT Digital Logic

More information

Chapter 2 Basic Logic Circuits and VHDL Description

Chapter 2 Basic Logic Circuits and VHDL Description Chapter 2 Basic Logic Circuits and VHDL Description We cannot solve our problems with the same thinking we used when we created them. ----- Albert Einstein Like a C or C++ programmer don t apply the logic.

More information

Computer Organization (Autonomous)

Computer Organization (Autonomous) Computer Organization (Autonomous) UNIT I Sections - A & D Prepared by Anil Kumar Prathipati, Asst. Prof., Dept. of CSE. SYLLABUS Introduction: Types of Computers, Functional units of Basic Computer (Block

More information

Propositional Calculus: Boolean Algebra and Simplification. CS 270: Mathematical Foundations of Computer Science Jeremy Johnson

Propositional Calculus: Boolean Algebra and Simplification. CS 270: Mathematical Foundations of Computer Science Jeremy Johnson Propositional Calculus: Boolean Algebra and Simplification CS 270: Mathematical Foundations of Computer Science Jeremy Johnson Propositional Calculus Topics Motivation: Simplifying Conditional Expressions

More information

CS 261 Fall Mike Lam, Professor. Logic Gates

CS 261 Fall Mike Lam, Professor. Logic Gates CS 261 Fall 2016 Mike Lam, Professor Logic Gates The final frontier Java programs running on Java VM C programs compiled on Linux Assembly / machine code on CPU + memory??? Switches and electric signals

More information

ECE3663 Design Project: Design Review #1

ECE3663 Design Project: Design Review #1 ECE3663 Design Project: Design Review #1 General Overview: For the first stage of the project, we designed four different components of the arithmetic logic unit. First, schematics for each component were

More information

Principles of Digital Techniques PDT (17320) Assignment No State advantages of digital system over analog system.

Principles of Digital Techniques PDT (17320) Assignment No State advantages of digital system over analog system. Assignment No. 1 1. State advantages of digital system over analog system. 2. Convert following numbers a. (138.56) 10 = (?) 2 = (?) 8 = (?) 16 b. (1110011.011) 2 = (?) 10 = (?) 8 = (?) 16 c. (3004.06)

More information

Reference Sheet for C112 Hardware

Reference Sheet for C112 Hardware Reference Sheet for C112 Hardware 1 Boolean Algebra, Gates and Circuits Autumn 2016 Basic Operators Precedence : (strongest),, + (weakest). AND A B R 0 0 0 0 1 0 1 0 0 1 1 1 OR + A B R 0 0 0 0 1 1 1 0

More information

Logic, Words, and Integers

Logic, Words, and Integers Computer Science 52 Logic, Words, and Integers 1 Words and Data The basic unit of information in a computer is the bit; it is simply a quantity that takes one of two values, 0 or 1. A sequence of k bits

More information

EECS150, Fall 2004, Midterm 1, Prof. Culler. Problem 1 (15 points) 1.a. Circle the gate-level circuits that DO NOT implement a Boolean AND function.

EECS150, Fall 2004, Midterm 1, Prof. Culler. Problem 1 (15 points) 1.a. Circle the gate-level circuits that DO NOT implement a Boolean AND function. Problem 1 (15 points) 1.a. Circle the gate-level circuits that DO NOT implement a Boolean AND function. 1.b. Show that a 2-to-1 MUX is universal (i.e. that any Boolean expression can be implemented with

More information

Introduction to Digital Logic Missouri S&T University CPE 2210 Registers

Introduction to Digital Logic Missouri S&T University CPE 2210 Registers Introduction to Digital Logic Missouri S&T University CPE 2210 Registers Egemen K. Çetinkaya Department of Electrical & Computer Engineering Missouri University of Science and Technology cetinkayae@mst.edu

More information

Lec-6-HW-3-ALUarithmetic-SOLN

Lec-6-HW-3-ALUarithmetic-SOLN Lec-6-HW-3-ALUarithmetic-SOLN Reading, PP, Chp 2: 2.1 (Bits and datatypes) 2.2 (signed and unsigned integers) 2.3 (2's complement) 2.4 (positional notation) 2.5 (int. add/sub, signed/unsigned overflow)

More information

Arithmetic Logic Unit. Digital Computer Design

Arithmetic Logic Unit. Digital Computer Design Arithmetic Logic Unit Digital Computer Design Arithmetic Circuits Arithmetic circuits are the central building blocks of computers. Computers and digital logic perform many arithmetic functions: addition,

More information

R a) Simplify the logic functions from binary to seven segment display code converter (8M) b) Simplify the following using Tabular method

R a) Simplify the logic functions from binary to seven segment display code converter (8M) b) Simplify the following using Tabular method SET - 1 1. a) Convert the decimal number 250.5 to base 3, base 4 b) Write and prove de-morgan laws c) Implement two input EX-OR gate from 2 to 1 multiplexer (3M) d) Write the demerits of PROM (3M) e) What

More information

Review. EECS Components and Design Techniques for Digital Systems. Lec 05 Boolean Logic 9/4-04. Seq. Circuit Behavior. Outline.

Review. EECS Components and Design Techniques for Digital Systems. Lec 05 Boolean Logic 9/4-04. Seq. Circuit Behavior. Outline. Review EECS 150 - Components and Design Techniques for Digital Systems Lec 05 Boolean Logic 94-04 David Culler Electrical Engineering and Computer Sciences University of California, Berkeley Design flow

More information