Computer Science. 19. Combinational Circuits. Computer Science. Building blocks Boolean algebra Digital circuits Adder circuit. Arithmetic/logic unit

Size: px
Start display at page:

Download "Computer Science. 19. Combinational Circuits. Computer Science. Building blocks Boolean algebra Digital circuits Adder circuit. Arithmetic/logic unit"

Transcription

1 PA R T I I : A L G O R I T H M S, M A C H I N E S, a n d T H E O R Y PA R T I I : A L G O R I T H M S, M A C H I N E S, a n d T H E O R Y Computer Science 9. Combinational Circuits Computer Science 9. Combinational Circuits Building blocks Boolean algebra Digital circuits Adder circuit An Interdisciplinary Approach Section 6. Arithmetic/logic unit ROBERT SEDGEWICK K E V I N WAY N E CS.9.A.Circuits.Basics Context Wires Wires propagate on/off values ON (): connected to power. OFF (): not connected to power. Any wire connected to a wire that is ON is also ON. Drawing convention: "flow" from top, left to bottom, right. Q. What is a combinational circuit? A. A digital circuit (all signals are or ) with no feedback (no loops). analog circuit: signals vary continuously sequential circuit: loops allowed (stay tuned) Q. Why combinational circuits? A. Accurate, reliable, general purpose, fast, cheap. thick wires are ON Basic abstractions power connection On and off. Wire: propagates on/off value. Switch: controls propagation of on/off values through wires. thin wires are OFF Applications. Smartphone, tablet, game controller, antilock brakes, microprocessor,

2 Controlled Switch Controlled Switch Switches control propagation of on/off values through wires. Simplest case involves two connections: control (input) and. control OFF: ON control ON: OFF Switches control propagation of on/off values through wires. General case involves three connections: control input, data input and. control OFF: is connected to input control ON: is disconnected from input control input OFF control input OFF data input OFF control input ON control input ON OFF data input OFF control input OFF ON control input ON OFF data input ON 5 Controlled switch: example implementation ON data input ON Idealized model of pass transistors found in real integrated circuits. OFF 6 First level of abstraction A relay is a physical device that controls a switch with a magnet connections: input,, control. Magnetic force pulls on a contact that cuts electrical flow. schematic OFF control off Switches and wires model provides separation between physical world and logical world. We assume that switches operate as specified. That is the only assumption. Physical realization of switch is irrelevant to design. control on magnet (off ) contact connection broken Physical realization dictates performance Size. Speed. Power. magnet on pulls contact up New technology immediately gives new computer. spring Better switch? Better computer. Basis of Moore's law. 7 all built with "switches and wires" 8

3 Switches and wires: a first level of abstraction Switches and wires: a first level of abstraction technology technology information pneumatic air pressure switch switch VLSI = Very Large Scale Integration relay (9s) Technology Deposit materials on substrate. Key properties Lines are wires. Certain crossing lines are controlled switches. vacuum tube fluid relay (now) water pressure electric potential Amusing attempts that do not scale but prove the point Key challenge in physical world Fabricating physical circuits with billions of wires and controlled switches transistor pass transistor in integrated circuit Key challenge in abstract world Understanding behavior of circuits with billions of wires and controlled switches atom-thick transistor Bottom line. Circuit = Drawing (!) Real-world examples that prove the point 9 Circuit anatomy Image sources Need more levels of abstraction to understand circuit behavior CS.9.A.Circuits.Basics

4 PART II: ALGORITHMS, MACHINES, and THEORY Boolean algebra Developed by George Boole in 8s to study logic problems Variables represent true or false ( or for short). Basic operations are AND, OR, and NOT (see table below). Widely used in mathematics, logic and computer science. 9. Combinational Circuits Building blocks Boolean algebra Digital circuits Adder circuit Arithmetic/logic unit operation Java notation logic notation circuit design (this lecture) AND x && y x y xy OR x y x y x + y NOT! x x x' Example: (stay tuned for proof) DeMorgan's Laws (xy)' = (x' + y' ) (x + y)' = x'y' various notations in common use George Boole CS.9.B.Circuits.Algebra Relevance to circuits. Basis for next level of abstraction. Copyright, Sidney Harris Truth tables Truth table proofs A truth table is a systematic way to define a Boolean function One row for each possible set of arguments. Each row gives the function value for the specified arguments. N inputs: N rows needed. Truth tables are convenient for establishing identities in Boolean logic One row for each possibility. Identity established if columns match. x x' NOT x y xy x y x + y x y NOR x y XOR Proofs of DeMorgan's laws x y xy (xy) ' x y x' y' x' + y' x y x + y NOR (x + y)' NOR x y x' y' x'y' AND OR NOR XOR (xy)' = (x' + y' ) (x + y)' = x'y' 5 6

5 All Boolean functions of two variables Functions of three and more variables Q. How many Boolean functions of two variables? A. 6 (all possibilities for the bits in the truth table column). Q. How many Boolean functions of three variables? A. 56 (all possibilities for the 8 bits in the truth table column). Truth tables for all Boolean functions of variables x y ZERO AND x y XOR OR NOR EQ y x NAND ONE 7 AND OR NOR MAJ ODD Some Boolean functions of variables Examples AND logical AND iff any inputs is ( iff all inputs ) OR logical OR iff any input is ( iff all inputs ) NOR logical NOR iff any input is ( iff all inputs ) MAJ majority iff more inputs are than ODD odd parity iff an odd number of inputs are Q. How many Boolean functions of N variables? A. (N ) N all extend to N variables number of Boolean functions with N variables = 6 8 = 56 6 = 65,56 5 =,9,967, = 8,6,7,7,79,55,66 8 Universality of AND, OR and NOT Every Boolean function can be represented as a sum of products Form an AND term for each in Boolean function. OR all the terms together. Image sources MAJ x'yz xy'z xyz' xyz x'yz + xy'z + xyz' + xyz = MAJ Def. A set of operations is universal if every Boolean function can be expressed using just those operations. Fact. { AND, OR, NOT } is universal. Expressing MAJ as a sum of products 9 CS.9.B.Circuits.Algebra

6 PART II: ALGORITHMS, MACHINES, and THEORY A basis for digital devices Claude Shannon connected circuit design with Boolean algebra in Combinational Circuits Building blocks Boolean algebra Digital circuits Adder circuit Arithmetic/logic unit Possibly the most important, and also the most famous, master's thesis of the [th] Howard Gardner Key idea. Can use Boolean algebra to systematically analyze circuit behavior. Claude Shannon 96 CS.9.C.Circuits.Digital A second level of abstraction: logic gates Multiway OR gates boolean function NOT notation x' truth table x x' classic symbol x our symbol x' under the cover circuit (gate) x x' proof iff x is OR gates with multiple inputs. if any input is. if all inputs are. NOR (x + y)' x y NOR (x+y)' x y NOR (x+y)' x y (x+y)' iff x and y are both classic symbol u v w u+v+w+x+y+z our symbol u v w OR u+v+w+x+y+z under the cover u v w if inputs are ; if any input is u+v+w+x+y+z OR AND x + y xy x y OR x y AND x y OR x y AND x+y xy x y x y x+y xy NOR x+y = ((x + y)')' NOR xy = (x' + y')' Multiway OR gates are oriented vertically in our circuits. Learn to recognize them! examples

7 Multiway generalized AND gates Multiway generalized AND gates. for exactly set of input values. for all other sets of input values. Pop quiz on generalized AND gates Q. Give the Boolean function computed by these gates. Q. Also give the inputs for which the is. gate u v w function inputs that another set of inputs u v w AND uvwxyz u v w u v w generalized u'vwx'y'z NOR u v w u'v'w'x'y'z' same as (u + v + w + x + y + z)' Might also call these "generalized NOR gates"; we consistently use AND. 5 6 Pop quiz on generalized AND gates A useful combinational circuit: decoder Q. Give the Boolean function computed by these gates. Q. Also give the inputs for which the is. u v w uv'wxy'z x'y'z' x'y'z x'yz' Decoder n input lines (address). n s. Addressed is. All other s are. Example: -to-8 decoder = 6 u v w u'vwx'y'z x'yz xy'z' s -5 and 7 are Get the idea? If not, replay this slide, like flash cards. Note. From now on, we will not label these gates. xy'z xyz' xyz is 7 8

8 A useful combinational circuit: decoder Decoder n input lines (address). n s. Addressed is. All other s are. Example: -to-8 decoder = 6 Another useful combinational circuit: demultiplexer (demux) Demultiplexer n address inputs. data input with value x. n s. Addressed has value x. All other s are. Example: -to-8 demux = 5 x Implementation Use all n generalized AND gates with n inputs. Only one of them matches the input address. s -5 and 7 are s - and 6-7 are 5 5 has value x Application (next lecture) Select a memory word for read/write. [Use address bits of instruction from IR.] 6 is Another useful combinational circuit: demultiplexer (demux) Demultiplexer n address inputs. data input with value x. n s. Addressed has value x. All other s are. Example: -to-8 demux = 5 x Decoder/demux Decoder/demux n address inputs. data input with value x. n pairs. Addressed pair has value (, x ). All other s are. = 5 x Example: -to-8 decoder/demux Implementation Start with decoder. Add AND x to each gate. s - and 6-7 are pairs - and 6-7 are (, ) 5 5 has value x 5 pair 5 has value (, x) Application (next lecture) Turn on control wires to implement instructions. [Use opcode bits of instruction in IR.]

9 Decoder/demux Decoder/demux n address inputs. data input with value x. n pairs. Addressed pair has value (, x ). All other s are. Example: -to-8 decoder/demux = 5 x Creating a digital circuit that computes a boolean function: majority Use the truth table Identify rows where the function is. Use a generalized AND gate for each. OR the results together. Example : Majority function MAJ xyz multiway OR gate MAJ Implementation Add decoder to demux. pairs - and 6-7 are (, ) term gate pair 5 has value (, x) x'yz Application (next lecture) Access and control write of memory word [Use addr bits of instruction in IR.] MAJ = x'yz + xy'z + xyz' + xyz xy'z xyz' xyz MAJ majority circuit example MAJ is Creating a digital circuit that computes a boolean function: odd parity Combinational circuit design: Summary Use the truth table Identify rows where the function is. Use a generalized AND gate for each. OR the results together. Example : Odd parity function ODD term x'y'z x'yz' xy'z' gate xyz multiway OR gate ODD Problem: Design a circuit that computes a given boolean function. Ingredients OR gates. NOT gates. NOR gates. Wire. use to make generalized AND gates Method Step : Represent input and with Boolean variables. Step : Construct truth table to define the function. Step : Identify rows where the function is. Step : Use a generalized AND for each and OR the results. MAJ xyz MAJ ODD xyz ODD ODD = x'y'z + x'yz' + xy'z' + xyz xyz ODD odd parity circuit example ODD is 5 Bottom line (profound idea): Yields a circuit for ANY function. Caveat: Circuit might be huge (stay tuned). MAJ ODD 6

10 Pop quiz on combinational circuit design Q. Design a circuit to implement XOR(x, y). Pop quiz on combinational circuit design Q. Design a circuit to implement XOR(x, y). A. Use the truth table Identify rows where the function is. Use a generalized AND gate for each. OR the results together. XOR function circuit interface x y XOR xy term gate x'y xy' XOR = x'y + xy' XOR XOR 7 8 Encapsulation Encapsulation in hardware design mirrors familiar principles in software design Building a circuit from wires and switches is the implementation. Define a circuit by its inputs, controls, and s is the API. We control complexity by encapsulating circuits as we do with ADTs. Image sources NOT AND DECODER DEMULTIPLEXER DECODER/DEMUX ODD OR MAJ XOR 9 CS.9.C.Circuits.Digital

11 Let's make an adder circuit! 9. Combinational Circuits PART II: ALGORITHMS, MACHINES, and THEORY Adder Compute z = x + y for n-bit binary integers. n inputs. n s. Ignore overflow. ADD + 9 Building blocks Boolean algebra Digital circuits Adder circuit Arithmetic/logic unit carry out Example: 8-bit adder + CS.9.D.Circuits.Adder = 7 Let's make an adder circuit! Let's make an adder circuit! Adder Compute z = x + y for n-bit binary integers. n inputs. n s. Ignore overflow. x7 y7 x6 y6 x5 y5 x y x y x y x y x y ADD Goal: z = x + y for 8-bit integers. Strawman solution: Build truth tables for each bit. x7 x6 x5 x x x x x y7 y6 y5 y y y y y c z7 z6 z5 z z z z z c8 c7 c6 c5 c c c c x7 x6 x5 x x x x x + y7 y6 y5 y y y y y z7 z6 z5 z z z z z Example: 8-bit adder 8-bit adder truth table 6 = 6556 rows! carry out c8 c7 c6 c5 c c c c x7 x6 x5 x x x x x + y7 y6 y5 y y y y y z7 z6 z5 z z z z z Q. Not convinced this a bad idea? z7 z6 z5 z z z z z A. 8-bit adder: 56 rows >> # electrons in universe!

12 Let's make an adder circuit! Let's make an adder circuit! Goal: z = x + y for 8-bit integers. Do one bit at a time. Build truth table for carry bit. Build truth table for sum bit. carry bit xi yi ci ci+ MAJ A surprise! Carry bit is MAJ. Sum bit is ODD. sum bit xi yi ci zi c8 c7 c6 c5 c c c c x7 x6 x5 x x x x x + y7 y6 y5 y y y y y z7 z6 z5 z z z z z ODD Goal: z = x + y for -bit integers. Do one bit at a time. Carry bit is MAJ. Sum bit is ODD. Chain -bit adders to "ripple" carries. c8 c7 c6 c5 c c c c x7 x6 x5 x x x x x + y7 y6 y5 y y y y y z7 z6 z5 z z z z z x7 y7 x6 y6 x5 y5 x y x y x y x y x y c7 c6 c5 c c c c c z7 z6 z5 z z z z z 5 6 An 8-bit adder circuit Layers of abstraction Lessons for software design apply to hardware Interface describes behavior of circuit. Implementation gives details of how to build it. Exploit understanding of behavior at each level. Layers of abstraction apply with a vengeance On/off. Controlled switch. [relay, pass transistor] Gates. [NOT, OR, AND] Boolean functions. [MAJ, ODD] Adder. Arithmetic/Logic unit (next). CPU (next lecture, stay tuned). ADD NOT OR AND MAJ ODD Vastly simplifies design of complex systems and enables use of new technology at any layer 7 8

13 PART II: ALGORITHMS, MACHINES, and THEORY 9. Combinational Circuits Building blocks Boolean algebra Digital circuits Adder circuit Arithmetic/logic unit CS.9.D.Circuits.Adder CS.9.E.Circuits.ALU Next layer of abstraction: modules, busses, and control lines Arithmetic and logic unit (ALU) module Basic design of our circuits Organized as modules (functional units of TOY: ALU, memory, register, PC, and IR). Connected by busses (groups of wires that propagate information between modules). Controlled by control lines (single wires that control circuit behavior). Ex. Three functions on 8-bit words Two input busses (arguments). One bus (result). Three control lines. input busses ALU (8-bit) Conventions Bus inputs are at the top, input connections are at the left. Bus s are at the bottom, connections are at the right. Control lines are blue. input busses control lines control lines ADD XOR These conventions make circuits easy to understand. (Like style conventions in coding.) bus 5 AND bus 5

14 Arithmetic and logic unit (ALU) module A simple and useful combinational circuit: one-hot multiplexer Ex. Three functions on 8-bit words Two input busses (arguments). One bus (result). Three control lines. Left-right shifter circuits omitted (see book for details). input busses One-hot multiplexer m selection lines m data inputs. At most one selection line is. Output has value of selected input. selection inputs this is a precondition unlike other circuits we consider select input data input is all other data inputs ignored Implementation One circuit for each function. Compute all values in parallel. ADD is Q. How do we select desired? A. "One-hot muxes" (see next slide). control lines XOR AND data inputs data input is "Calculator" at the heart of your computer. bus 5 is 5 A simple and useful combinational circuit: one-hot multiplexer One-hot multiplexer m selection lines m data inputs. At most one selection line is. Output has value of selected input. Implementation AND corresponding selection and data inputs. OR all results (at most one is ). AND gate multiway OR gate select input data input is is Summary: Useful combinational circuit modules DEMUX DECODER/DEMUX ALU Applications Arithmetic-logic unit (previous slide). Main memory (next lecture). data input is Important to note. No direct connection from input to. a virtual selection switch is 55 Next: Registers, memory, connections, and control. 56

15 PA R T I I : A L G O R I T H M S, M A C H I N E S, a n d T H E O R Y Computer Science Computer Science An Interdisciplinary Approach Section 6. ROBERT SEDGEWICK K E V I N WAY N E CS.9.D.Circuits.Adder 9. Combinational Circuits

CHAPTER 3 Boolean Algebra and Digital Logic

CHAPTER 3 Boolean Algebra and Digital Logic CHAPTER 3 Boolean Algebra and Digital Logic 3.1 Introduction 121 3.2 Boolean Algebra 122 3.2.1 Boolean Expressions 123 3.2.2 Boolean Identities 124 3.2.3 Simplification of Boolean Expressions 126 3.2.4

More information

Digital Logic Design. Basics Combinational Circuits Sequential Circuits. Pu-Jen Cheng

Digital Logic Design. Basics Combinational Circuits Sequential Circuits. Pu-Jen Cheng Digital Logic Design Basics Combinational Circuits Sequential Circuits Pu-Jen Cheng Adapted from the slides prepared by S. Dandamudi for the book, Fundamentals of Computer Organization and Design. Introduction

More information

Gates, Circuits, and Boolean Algebra

Gates, Circuits, and Boolean Algebra Gates, Circuits, and Boolean Algebra Computers and Electricity A gate is a device that performs a basic operation on electrical signals Gates are combined into circuits to perform more complicated tasks

More information

1. True or False? A voltage level in the range 0 to 2 volts is interpreted as a binary 1.

1. True or False? A voltage level in the range 0 to 2 volts is interpreted as a binary 1. File: chap04, Chapter 04 1. True or False? A voltage level in the range 0 to 2 volts is interpreted as a binary 1. 2. True or False? A gate is a device that accepts a single input signal and produces one

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

Chapter 4. Gates and Circuits. Chapter Goals. Chapter Goals. Computers and Electricity. Computers and Electricity. Gates

Chapter 4. Gates and Circuits. Chapter Goals. Chapter Goals. Computers and Electricity. Computers and Electricity. Gates Chapter Goals Chapter 4 Gates and Circuits Identify the basic gates and describe the behavior of each Describe how gates are implemented using transistors Combine basic gates into circuits Describe the

More information

l What have discussed up until now & why: l C Programming language l More low-level then Java. l Better idea about what s really going on.

l What have discussed up until now & why: l C Programming language l More low-level then Java. l Better idea about what s really going on. CS211 Computer Architecture l Topics Digital Logic l Transistors (Design & Types) l Logic Gates l Combinational Circuits l K-Maps Class Checkpoint l What have discussed up until now & why: l C Programming

More information

Chapter 5: Sequential Circuits (LATCHES)

Chapter 5: Sequential Circuits (LATCHES) Chapter 5: Sequential Circuits (LATCHES) Latches We focuses on sequential circuits, where we add memory to the hardware that we ve already seen Our schedule will be very similar to before: We first show

More information

Let s put together a Manual Processor

Let s put together a Manual Processor Lecture 14 Let s put together a Manual Processor Hardware Lecture 14 Slide 1 The processor Inside every computer there is at least one processor which can take an instruction, some operands and produce

More information

Understanding Logic Design

Understanding Logic Design Understanding Logic Design ppendix of your Textbook does not have the needed background information. This document supplements it. When you write add DD R0, R1, R2, you imagine something like this: R1

More information

Chapter 4 Register Transfer and Microoperations. Section 4.1 Register Transfer Language

Chapter 4 Register Transfer and Microoperations. Section 4.1 Register Transfer Language Chapter 4 Register Transfer and Microoperations Section 4.1 Register Transfer Language Digital systems are composed of modules that are constructed from digital components, such as registers, decoders,

More information

Combinational circuits

Combinational circuits Combinational circuits Combinational circuits are stateless The outputs are functions only of the inputs Inputs Combinational circuit Outputs 3 Thursday, September 2, 3 Enabler Circuit (High-level view)

More information

8-bit 4-to-1 Line Multiplexer

8-bit 4-to-1 Line Multiplexer Project Part I 8-bit 4-to-1 Line Multiplexer Specification: This section of the project outlines the design of a 4-to-1 multiplexor which takes two 8-bit buses as inputs and produces a single 8-bit bus

More information

Logic in Computer Science: Logic Gates

Logic in Computer Science: Logic Gates Logic in Computer Science: Logic Gates Lila Kari The University of Western Ontario Logic in Computer Science: Logic Gates CS2209, Applied Logic for Computer Science 1 / 49 Logic and bit operations Computers

More information

Experiment 5. Arithmetic Logic Unit (ALU)

Experiment 5. Arithmetic Logic Unit (ALU) Experiment 5 Arithmetic Logic Unit (ALU) Objectives: To implement and test the circuits which constitute the arithmetic logic circuit (ALU). Background Information: The basic blocks of a computer are central

More information

exclusive-or and Binary Adder R eouven Elbaz reouven@uwaterloo.ca Office room: DC3576

exclusive-or and Binary Adder R eouven Elbaz reouven@uwaterloo.ca Office room: DC3576 exclusive-or and Binary Adder R eouven Elbaz reouven@uwaterloo.ca Office room: DC3576 Outline exclusive OR gate (XOR) Definition Properties Examples of Applications Odd Function Parity Generation and Checking

More information

Digital Logic: Boolean Algebra and Gates

Digital Logic: Boolean Algebra and Gates Digital Logic: Boolean Algebra and Gates Textbook Chapter 3 CMPE2 Summer 28 Basic Logic Gates CMPE2 Summer 28 Slides by ADB 2 Truth Table The most basic representation of a logic function Lists the output

More information

Digital Electronics Detailed Outline

Digital Electronics Detailed Outline Digital Electronics Detailed Outline Unit 1: Fundamentals of Analog and Digital Electronics (32 Total Days) Lesson 1.1: Foundations and the Board Game Counter (9 days) 1. Safety is an important concept

More information

Binary Adder. sum of 2 binary numbers can be larger than either number need a carry-out to store the overflow

Binary Adder. sum of 2 binary numbers can be larger than either number need a carry-out to store the overflow Binary Addition single bit addition Binary Adder sum of 2 binary numbers can be larger than either number need a carry-out to store the overflow Half-Adder 2 inputs (x and y) and 2 outputs (sum and carry)

More information

Chapter 2 Logic Gates and Introduction to Computer Architecture

Chapter 2 Logic Gates and Introduction to Computer Architecture Chapter 2 Logic Gates and Introduction to Computer Architecture 2.1 Introduction The basic components of an Integrated Circuit (IC) is logic gates which made of transistors, in digital system there are

More information

Integer multiplication

Integer multiplication Integer multiplication Suppose we have two unsigned integers, A and B, and we wish to compute their product. Let A be the multiplicand and B the multiplier: A n 1... A 1 A 0 multiplicand B n 1... B 1 B

More information

Sistemas Digitais I LESI - 2º ano

Sistemas Digitais I LESI - 2º ano Sistemas Digitais I LESI - 2º ano Lesson 6 - Combinational Design Practices Prof. João Miguel Fernandes (miguel@di.uminho.pt) Dept. Informática UNIVERSIDADE DO MINHO ESCOLA DE ENGENHARIA - PLDs (1) - The

More information

5 Combinatorial Components. 5.0 Full adder. Full subtractor

5 Combinatorial Components. 5.0 Full adder. Full subtractor 5 Combatorial Components Use for data transformation, manipulation, terconnection, and for control: arithmetic operations - addition, subtraction, multiplication and division. logic operations - AND, OR,

More information

Take-Home Exercise. z y x. Erik Jonsson School of Engineering and Computer Science. The University of Texas at Dallas

Take-Home Exercise. z y x. Erik Jonsson School of Engineering and Computer Science. The University of Texas at Dallas Take-Home Exercise Assume you want the counter below to count mod-6 backward. That is, it would count 0-5-4-3-2-1-0, etc. Assume it is reset on startup, and design the wiring to make the counter count

More information

Lab 1: Full Adder 0.0

Lab 1: Full Adder 0.0 Lab 1: Full Adder 0.0 Introduction In this lab you will design a simple digital circuit called a full adder. You will then use logic gates to draw a schematic for the circuit. Finally, you will verify

More information

CS 16: Assembly Language Programming for the IBM PC and Compatibles

CS 16: Assembly Language Programming for the IBM PC and Compatibles CS 16: Assembly Language Programming for the IBM PC and Compatibles First, a little about you Your name Have you ever worked with/used/played with assembly language? If so, talk about it Why are you taking

More information

Systems I: Computer Organization and Architecture

Systems I: Computer Organization and Architecture Systems I: Computer Organization and Architecture Lecture 9 - Register Transfer and Microoperations Microoperations Digital systems are modular in nature, with modules containing registers, decoders, arithmetic

More information

4 Combinational Components

4 Combinational Components Chapter 4 Combinational Components Page of 8 4 Combinational Components In constructing large digital circuits, instead of starting with the basic gates as building blocks, we often start with larger building

More information

3.Basic Gate Combinations

3.Basic Gate Combinations 3.Basic Gate Combinations 3.1 TTL NAND Gate In logic circuits transistors play the role of switches. For those in the TTL gate the conducting state (on) occurs when the baseemmiter signal is high, and

More information

Figure 8-1 Four Possible Results of Adding Two Bits

Figure 8-1 Four Possible Results of Adding Two Bits CHPTER EIGHT Combinational Logic pplications Thus far, our discussion has focused on the theoretical design issues of computer systems. We have not yet addressed any of the actual hardware you might find

More information

Lecture #21 April 2, 2004 Relays and Adder/Subtractors

Lecture #21 April 2, 2004 Relays and Adder/Subtractors Lecture #21 April 2, 2004 Relays and Adder/Subtractors In this lecture we look at a real technology for implementing gate circuits, as well as a more-or-less complete design for a general purpose adder/subtractor

More information

Circuits and Boolean Expressions

Circuits and Boolean Expressions Circuits and Boolean Expressions Provided by TryEngineering - Lesson Focus Boolean logic is essential to understanding computer architecture. It is also useful in program construction and Artificial Intelligence.

More information

(Refer Slide Time: 00:01:16 min)

(Refer Slide Time: 00:01:16 min) Digital Computer Organization Prof. P. K. Biswas Department of Electronic & Electrical Communication Engineering Indian Institute of Technology, Kharagpur Lecture No. # 04 CPU Design: Tirning & Control

More information

Two-level logic using NAND gates

Two-level logic using NAND gates CSE140: Components and Design Techniques for Digital Systems Two and Multilevel logic implementation Tajana Simunic Rosing 1 Two-level logic using NND gates Replace minterm ND gates with NND gates Place

More information

COMBINATIONAL CIRCUITS

COMBINATIONAL CIRCUITS COMBINATIONAL CIRCUITS http://www.tutorialspoint.com/computer_logical_organization/combinational_circuits.htm Copyright tutorialspoint.com Combinational circuit is a circuit in which we combine the different

More information

#5. Show and the AND function can be constructed from two NAND gates.

#5. Show and the AND function can be constructed from two NAND gates. Study Questions for Digital Logic, Processors and Caches G22.0201 Fall 2009 ANSWERS Digital Logic Read: Sections 3.1 3.3 in the textbook. Handwritten digital lecture notes on the course web page. Study

More information

CSE140 Homework #7 - Solution

CSE140 Homework #7 - Solution CSE140 Spring2013 CSE140 Homework #7 - Solution You must SHOW ALL STEPS for obtaining the solution. Reporting the correct answer, without showing the work performed at each step will result in getting

More information

FORDHAM UNIVERSITY CISC 3593. Dept. of Computer and Info. Science Spring, 2011. Lab 2. The Full-Adder

FORDHAM UNIVERSITY CISC 3593. Dept. of Computer and Info. Science Spring, 2011. Lab 2. The Full-Adder FORDHAM UNIVERSITY CISC 3593 Fordham College Lincoln Center Computer Organization Dept. of Computer and Info. Science Spring, 2011 Lab 2 The Full-Adder 1 Introduction In this lab, the student will construct

More information

Transparent D Flip-Flop

Transparent D Flip-Flop Transparent Flip-Flop The RS flip-flop forms the basis of a number of 1-bit storage devices in digital electronics. ne such device is shown in the figure, where extra combinational logic converts the input

More information

ECE410 Design Project Spring 2008 Design and Characterization of a CMOS 8-bit Microprocessor Data Path

ECE410 Design Project Spring 2008 Design and Characterization of a CMOS 8-bit Microprocessor Data Path ECE410 Design Project Spring 2008 Design and Characterization of a CMOS 8-bit Microprocessor Data Path Project Summary This project involves the schematic and layout design of an 8-bit microprocessor data

More information

Combinational Logic. Combinational Circuits in Computers (Examples) Design of Combinational Circuits. CC Design Example

Combinational Logic. Combinational Circuits in Computers (Examples) Design of Combinational Circuits. CC Design Example Combinational Circuits in Computers (Examples) Combinational Logic Translates a set of Boolean n input variables ( or ) by a mapping function (using Boolean operations) to produce a set of Boolean m output

More information

Basic Logic Gates Richard E. Haskell

Basic Logic Gates Richard E. Haskell BASIC LOGIC GATES 1 E Basic Logic Gates Richard E. Haskell All digital systems are made from a few basic digital circuits that we call logic gates. These circuits perform the basic logic functions that

More information

Lecture 5: Gate Logic Logic Optimization

Lecture 5: Gate Logic Logic Optimization Lecture 5: Gate Logic Logic Optimization MAH, AEN EE271 Lecture 5 1 Overview Reading McCluskey, Logic Design Principles- or any text in boolean algebra Introduction We could design at the level of irsim

More information

A single register, called the accumulator, stores the. operand before the operation, and stores the result. Add y # add y from memory to the acc

A single register, called the accumulator, stores the. operand before the operation, and stores the result. Add y # add y from memory to the acc Other architectures Example. Accumulator-based machines A single register, called the accumulator, stores the operand before the operation, and stores the result after the operation. Load x # into acc

More information

C H A P T E R. Logic Circuits

C H A P T E R. Logic Circuits C H A P T E R Logic Circuits Many important functions are naturally computed with straight-line programs, programs without loops or branches. Such computations are conveniently described with circuits,

More information

ENEE 244 (01**). Spring 2006. Homework 4. Due back in class on Friday, April 7.

ENEE 244 (01**). Spring 2006. Homework 4. Due back in class on Friday, April 7. ENEE 244 (**). Spring 26 Homework 4 Due back in class on Friday, April 7.. Implement the following Boolean expression with exclusive-or and AND gates only: F = AB'CD' + A'BCD' + AB'C'D + A'BC'D. F = AB

More information

CISC 310 ONLINE Spring 2016. Review for Final Exam

CISC 310 ONLINE Spring 2016. Review for Final Exam CISC 310 ONLINE Spring 2016 Review for Final Exam The following is a study guide to help you prepare for the exam. The exam will include but not be limited to the information on this review sheet. The

More information

EE360: Digital Design I Course Syllabus

EE360: Digital Design I Course Syllabus : Course Syllabus Dr. Mohammad H. Awedh Fall 2008 Course Description This course introduces students to the basic concepts of digital systems, including analysis and design. Both combinational and sequential

More information

UNIT III CONTROL UNIT DESIGN

UNIT III CONTROL UNIT DESIGN UNIT III CONTROL UNIT DESIGN INTRODUCTION CONTROL TRANSFER FETCH CYCLE INSTRUCTION INTERPRETATION AND EXECUTION HARDWIRED CONTROL MICROPROGRAMMED CONTROL Slides Courtesy of Carl Hamacher, Computer Organization,

More information

Chapter 4. Arithmetic for Computers

Chapter 4. Arithmetic for Computers Chapter 4 Arithmetic for Computers Arithmetic Where we've been: Performance (seconds, cycles, instructions) What's up ahead: Implementing the Architecture operation a b 32 32 ALU 32 result 2 Constructing

More information

MICROPROCESSOR AND MICROCOMPUTER BASICS

MICROPROCESSOR AND MICROCOMPUTER BASICS Introduction MICROPROCESSOR AND MICROCOMPUTER BASICS At present there are many types and sizes of computers available. These computers are designed and constructed based on digital and Integrated Circuit

More information

what operations can it perform? how does it perform them? on what kind of data? where are instructions and data stored?

what operations can it perform? how does it perform them? on what kind of data? where are instructions and data stored? Inside the CPU how does the CPU work? what operations can it perform? how does it perform them? on what kind of data? where are instructions and data stored? some short, boring programs to illustrate the

More information

United States Naval Academy Electrical and Computer Engineering Department. EC262 Exam 1

United States Naval Academy Electrical and Computer Engineering Department. EC262 Exam 1 United States Naval Academy Electrical and Computer Engineering Department EC262 Exam 29 September 2. Do a page check now. You should have pages (cover & questions). 2. Read all problems in their entirety.

More information

CPU Organisation and Operation

CPU Organisation and Operation CPU Organisation and Operation The Fetch-Execute Cycle The operation of the CPU 1 is usually described in terms of the Fetch-Execute cycle. 2 Fetch-Execute Cycle Fetch the Instruction Increment the Program

More information

Computer organization

Computer organization Computer organization Computer design an application of digital logic design procedures Computer = processing unit + memory system Processing unit = control + datapath Control = finite state machine inputs

More information

Karnaugh Maps. Circuit-wise, this leads to a minimal two-level implementation

Karnaugh Maps. Circuit-wise, this leads to a minimal two-level implementation Karnaugh Maps Applications of Boolean logic to circuit design The basic Boolean operations are AND, OR and NOT These operations can be combined to form complex expressions, which can also be directly translated

More information

Computer Architecture

Computer Architecture Computer Architecture Having studied numbers, combinational and sequential logic, and assembly language programming, we begin the study of the overall computer system. The term computer architecture is

More information

Gates & Boolean Algebra. Boolean Operators. Combinational Logic. Introduction

Gates & Boolean Algebra. Boolean Operators. Combinational Logic. Introduction Introduction Gates & Boolean lgebra Boolean algebra: named after mathematician George Boole (85 864). 2-valued algebra. digital circuit can have one of 2 values. Signal between and volt =, between 4 and

More information

Lecture 12: More on Registers, Multiplexers, Decoders, Comparators and Wot- Nots

Lecture 12: More on Registers, Multiplexers, Decoders, Comparators and Wot- Nots Lecture 12: More on Registers, Multiplexers, Decoders, Comparators and Wot- Nots Registers As you probably know (if you don t then you should consider changing your course), data processing is usually

More information

BOOLEAN ALGEBRA & LOGIC GATES

BOOLEAN ALGEBRA & LOGIC GATES BOOLEAN ALGEBRA & LOGIC GATES Logic gates are electronic circuits that can be used to implement the most elementary logic expressions, also known as Boolean expressions. The logic gate is the most basic

More information

Digital Systems CCPS1573

Digital Systems CCPS1573 1. Name of Course 2. Course Code 3. Name(s) of academic staff 4. Rationale for the inclusion of the course/module in the programme Digital Systems CCPS1573 Faculty This module provides foundation knowledge

More information

CS101 Lecture 26: Low Level Programming. John Magee 30 July 2013 Some material copyright Jones and Bartlett. Overview/Questions

CS101 Lecture 26: Low Level Programming. John Magee 30 July 2013 Some material copyright Jones and Bartlett. Overview/Questions CS101 Lecture 26: Low Level Programming John Magee 30 July 2013 Some material copyright Jones and Bartlett 1 Overview/Questions What did we do last time? How can we control the computer s circuits? How

More information

Chapter 2 Combinational Logic Circuits

Chapter 2 Combinational Logic Circuits Logic and Computer Design Fundamentals Chapter 2 Combinational Logic Circuits Part 3 Additional Gates and Circuits Charles Kime & Thomas Kaminski 2008 Pearson Education, Inc. Overview Part 1 Gate Circuits

More information

LAB MANUAL SUBJECT: DIGITAL LOGIC DESIGN AND APPLICATIONS SE (COMPUTERS) SEM III

LAB MANUAL SUBJECT: DIGITAL LOGIC DESIGN AND APPLICATIONS SE (COMPUTERS) SEM III LAB MANUAL SUBJECT: DIGITAL LOGIC DESIGN AND APPLICATIONS SE (COMPUTERS) SEM III 1 INDEX Sr. No Title of the Experiment 1 Study of BASIC Gates 3 2 Universal Gates 6 3 Study of Full & Half Adder & Subtractor

More information

6.080/6.089 GITCS Feb 12, 2008. Lecture 3

6.080/6.089 GITCS Feb 12, 2008. Lecture 3 6.8/6.89 GITCS Feb 2, 28 Lecturer: Scott Aaronson Lecture 3 Scribe: Adam Rogal Administrivia. Scribe notes The purpose of scribe notes is to transcribe our lectures. Although I have formal notes of my

More information

CSE140: Components and Design Techniques for Digital Systems

CSE140: Components and Design Techniques for Digital Systems CSE4: Components and Design Techniques for Digital Systems Tajana Simunic Rosing What we covered thus far: Number representations Logic gates Boolean algebra Introduction to CMOS HW#2 due, HW#3 assigned

More information

Combinational Logic Design

Combinational Logic Design Chapter 4 Combinational Logic Design The foundations for the design of digital logic circuits were established in the preceding chapters. The elements of Boolean algebra (two-element switching algebra

More information

2011, The McGraw-Hill Companies, Inc. Chapter 4

2011, The McGraw-Hill Companies, Inc. Chapter 4 Chapter 4 4.1 The Binary Concept Binary refers to the idea that many things can be thought of as existing in only one of two states. The binary states are 1 and 0 The 1 and 0 can represent: ON or OFF Open

More information

FORDHAM UNIVERSITY CISC 3593. Dept. of Computer and Info. Science Spring, 2011. The Binary Adder

FORDHAM UNIVERSITY CISC 3593. Dept. of Computer and Info. Science Spring, 2011. The Binary Adder FORDHAM UNIVERITY CIC 3593 Fordham College Lincoln Center Computer Organization Dept. of Computer and Info. cience pring, 2011 1 Introduction The Binar Adder The binar adder circuit is an important building

More information

Chapter 2 Digital Components. Section 2.1 Integrated Circuits

Chapter 2 Digital Components. Section 2.1 Integrated Circuits Chapter 2 Digital Components Section 2.1 Integrated Circuits An integrated circuit (IC) is a small silicon semiconductor crystal, called a chip, containing the electronic components for the digital gates

More information

MICROPROCESSOR. Exclusive for IACE Students www.iace.co.in iacehyd.blogspot.in Ph: 9700077455/422 Page 1

MICROPROCESSOR. Exclusive for IACE Students www.iace.co.in iacehyd.blogspot.in Ph: 9700077455/422 Page 1 MICROPROCESSOR A microprocessor incorporates the functions of a computer s central processing unit (CPU) on a single Integrated (IC), or at most a few integrated circuit. It is a multipurpose, programmable

More information

Points Addressed in this Lecture

Points Addressed in this Lecture Points Addressed in this Lecture Lecture 3: Basic Logic Gates & Boolean Expressions Professor Peter Cheung Department of EEE, Imperial College London (Floyd 3.1-3.5, 4.1) (Tocci 3.1-3.9) What are the basic

More information

Building a computer. Electronic Numerical Integrator and Computer (ENIAC)

Building a computer. Electronic Numerical Integrator and Computer (ENIAC) Building a computer Electronic Numerical Integrator and Computer (ENIAC) CSCI 255: Introduc/on to Embedded Systems Keith Vertanen Copyright 2011 Layers of abstrac

More information

Gates. J. Robert Jump Department of Electrical And Computer Engineering Rice University Houston, TX 77251

Gates. J. Robert Jump Department of Electrical And Computer Engineering Rice University Houston, TX 77251 Gates J. Robert Jump Department of Electrical And Computer Engineering Rice University Houston, T 77251 1. The Evolution of Electronic Digital Devices...1 2. Logical Operations and the Behavior of Gates...2

More information

CHAPTER 2. Logic. 1. Logic Definitions. Notation: Variables are used to represent propositions. The most common variables used are p, q, and r.

CHAPTER 2. Logic. 1. Logic Definitions. Notation: Variables are used to represent propositions. The most common variables used are p, q, and r. CHAPTER 2 Logic 1. Logic Definitions 1.1. Propositions. Definition 1.1.1. A proposition is a declarative sentence that is either true (denoted either T or 1) or false (denoted either F or 0). Notation:

More information

Lab Manual. Digital System Design (Pr): COT-215 Digital Electronics (P): IT-211

Lab Manual. Digital System Design (Pr): COT-215 Digital Electronics (P): IT-211 Lab Manual Digital System Design (Pr): COT-215 Digital Electronics (P): IT-211 Lab Instructions Several practicals / programs? Whether an experiment contains one or several practicals /programs One practical

More information

The equation for the 3-input XOR gate is derived as follows

The equation for the 3-input XOR gate is derived as follows The equation for the 3-input XOR gate is derived as follows The last four product terms in the above derivation are the four 1-minterms in the 3-input XOR truth table. For 3 or more inputs, the XOR gate

More information

4 BOOLEAN ALGEBRA AND LOGIC SIMPLIFICATION

4 BOOLEAN ALGEBRA AND LOGIC SIMPLIFICATION 4 BOOLEAN ALGEBRA AND LOGIC SIMPLIFICATION BOOLEAN OPERATIONS AND EXPRESSIONS Variable, complement, and literal are terms used in Boolean algebra. A variable is a symbol used to represent a logical quantity.

More information

NEW adder cells are useful for designing larger circuits despite increase in transistor count by four per cell.

NEW adder cells are useful for designing larger circuits despite increase in transistor count by four per cell. CHAPTER 4 THE ADDER The adder is one of the most critical components of a processor, as it is used in the Arithmetic Logic Unit (ALU), in the floating-point unit and for address generation in case of cache

More information

Introduction. Logic. Most Difficult Reading Topics. Basic Logic Gates Truth Tables Logical Functions. COMP370 Introduction to Computer Architecture

Introduction. Logic. Most Difficult Reading Topics. Basic Logic Gates Truth Tables Logical Functions. COMP370 Introduction to Computer Architecture Introduction LOGIC GATES COMP370 Introduction to Computer Architecture Basic Logic Gates Truth Tables Logical Functions Truth Tables Logical Expression Graphical l Form Most Difficult Reading Topics Logic

More information

150127-Microprocessor & Assembly Language

150127-Microprocessor & Assembly Language Chapter 3 Z80 Microprocessor Architecture The Z 80 is one of the most talented 8 bit microprocessors, and many microprocessor-based systems are designed around the Z80. The Z80 microprocessor needs an

More information

CHAPTER TEN. 10.1 New Truth Table Symbols. 10.1.1 Edges/Transitions. Memory Cells

CHAPTER TEN. 10.1 New Truth Table Symbols. 10.1.1 Edges/Transitions. Memory Cells CHAPTER TEN Memory Cells The previous chapters presented the concepts and tools behind processing binary data. This is only half of the battle though. For example, a logic circuit uses inputs to calculate

More information

Chapter 6 Digital Arithmetic: Operations & Circuits

Chapter 6 Digital Arithmetic: Operations & Circuits Chapter 6 Digital Arithmetic: Operations & Circuits Chapter 6 Objectives Selected areas covered in this chapter: Binary addition, subtraction, multiplication, division. Differences between binary addition

More information

Computer System: User s View. Computer System Components: High Level View. Input. Output. Computer. Computer System: Motherboard Level

Computer System: User s View. Computer System Components: High Level View. Input. Output. Computer. Computer System: Motherboard Level System: User s View System Components: High Level View Input Output 1 System: Motherboard Level 2 Components: Interconnection I/O MEMORY 3 4 Organization Registers ALU CU 5 6 1 Input/Output I/O MEMORY

More information

Digital circuits make up all computers and computer systems. The operation of digital circuits is based on

Digital circuits make up all computers and computer systems. The operation of digital circuits is based on Digital Logic Circuits Digital circuits make up all computers and computer systems. The operation of digital circuits is based on Boolean algebra, the mathematics of binary numbers. Boolean algebra is

More information

Lab 1: Combinational Arithmetic Circuits CEG 360/560 - EE 451/651

Lab 1: Combinational Arithmetic Circuits CEG 360/560 - EE 451/651 Lab 1: Combinational Arithmetic Circuits CEG 360/560 - EE 451/651 PURPOSE The purpose of this introductory laboratory project is to familiarize students with the digital design and simulation software

More information

Binary Division. Decimal Division. Hardware for Binary Division. Simple 16-bit Divider Circuit

Binary Division. Decimal Division. Hardware for Binary Division. Simple 16-bit Divider Circuit Decimal Division Remember 4th grade long division? 43 // quotient 12 521 // divisor dividend -480 41-36 5 // remainder Shift divisor left (multiply by 10) until MSB lines up with dividend s Repeat until

More information

CHAPTER 7: The CPU and Memory

CHAPTER 7: The CPU and Memory CHAPTER 7: The CPU and Memory The Architecture of Computer Hardware, Systems Software & Networking: An Information Technology Approach 4th Edition, Irv Englander John Wiley and Sons 2010 PowerPoint slides

More information

1. Realization of gates using Universal gates

1. Realization of gates using Universal gates 1. Realization of gates using Universal gates Aim: To realize all logic gates using NAND and NOR gates. Apparatus: S. No Description of Item Quantity 1. IC 7400 01 2. IC 7402 01 3. Digital Trainer Kit

More information

DEPARTMENT OF INFORMATION TECHNLOGY

DEPARTMENT OF INFORMATION TECHNLOGY DRONACHARYA GROUP OF INSTITUTIONS, GREATER NOIDA Affiliated to Mahamaya Technical University, Noida Approved by AICTE DEPARTMENT OF INFORMATION TECHNLOGY Lab Manual for Computer Organization Lab ECS-453

More information

Adder.PPT(10/1/2009) 5.1. Lecture 13. Adder Circuits

Adder.PPT(10/1/2009) 5.1. Lecture 13. Adder Circuits Adder.T(//29) 5. Lecture 3 Adder ircuits Objectives Understand how to add both signed and unsigned numbers Appreciate how the delay of an adder circuit depends on the data values that are being added together

More information

INTRODUCTION TO DIGITAL SYSTEMS. IMPLEMENTATION: MODULES (ICs) AND NETWORKS IMPLEMENTATION OF ALGORITHMS IN HARDWARE

INTRODUCTION TO DIGITAL SYSTEMS. IMPLEMENTATION: MODULES (ICs) AND NETWORKS IMPLEMENTATION OF ALGORITHMS IN HARDWARE INTRODUCTION TO DIGITAL SYSTEMS 1 DESCRIPTION AND DESIGN OF DIGITAL SYSTEMS FORMAL BASIS: SWITCHING ALGEBRA IMPLEMENTATION: MODULES (ICs) AND NETWORKS IMPLEMENTATION OF ALGORITHMS IN HARDWARE COURSE EMPHASIS:

More information

Management Challenge. Managing Hardware Assets. Central Processing Unit. What is a Computer System?

Management Challenge. Managing Hardware Assets. Central Processing Unit. What is a Computer System? Management Challenge Managing Hardware Assets What computer processing and storage capability does our organization need to handle its information and business transactions? What arrangement of computers

More information

Lecture 8: Synchronous Digital Systems

Lecture 8: Synchronous Digital Systems Lecture 8: Synchronous Digital Systems The distinguishing feature of a synchronous digital system is that the circuit only changes in response to a system clock. For example, consider the edge triggered

More information

A s we saw in Chapter 4, a CPU contains three main sections: the register section,

A s we saw in Chapter 4, a CPU contains three main sections: the register section, 6 CPU Design A s we saw in Chapter 4, a CPU contains three main sections: the register section, the arithmetic/logic unit (ALU), and the control unit. These sections work together to perform the sequences

More information

Points Addressed in this Lecture. Standard form of Boolean Expressions. Lecture 5: Logic Simplication & Karnaugh Map

Points Addressed in this Lecture. Standard form of Boolean Expressions. Lecture 5: Logic Simplication & Karnaugh Map Points Addressed in this Lecture Lecture 5: Logic Simplication & Karnaugh Map Professor Peter Cheung Department of EEE, Imperial College London (Floyd 4.5-4.) (Tocci 4.-4.5) Standard form of Boolean Expressions

More information

Logic Design 2013/9/5. Introduction. Logic circuits operate on digital signals

Logic Design 2013/9/5. Introduction. Logic circuits operate on digital signals Introduction Logic Design Chapter 2: Introduction to Logic Circuits Logic circuits operate on digital signals Unlike continuous analog signals that have an infinite number of possible values, digital signals

More information

earlier in the semester: The Full adder above adds two bits and the output is at the end. So if we do this eight times, we would have an 8-bit adder.

earlier in the semester: The Full adder above adds two bits and the output is at the end. So if we do this eight times, we would have an 8-bit adder. The circuit created is an 8-bit adder. The 8-bit adder adds two 8-bit binary inputs and the result is produced in the output. In order to create a Full 8-bit adder, I could use eight Full -bit adders and

More information

4 Operations On Data

4 Operations On Data 4 Operations On Data 4.1 Source: Foundations of Computer Science Cengage Learning Objectives After studying this chapter, students should be able to: List the three categories of operations performed on

More information

CHAPTER 4 MARIE: An Introduction to a Simple Computer

CHAPTER 4 MARIE: An Introduction to a Simple Computer CHAPTER 4 MARIE: An Introduction to a Simple Computer 4.1 Introduction 195 4.2 CPU Basics and Organization 195 4.2.1 The Registers 196 4.2.2 The ALU 197 4.2.3 The Control Unit 197 4.3 The Bus 197 4.4 Clocks

More information