Computer Organization

Boolean Logic and the CPU

i206 Fall 2010

John Chuang

Some slides adapted from Marti Hearst, Brian Hayes, or Glenn Brookshear

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Boolean LogicCPU Operation

Bits & BytesBinary Numbers

Number Systems

Gates

Boolean Logic

Circuits

CPU Machine Instructions

Assembly Instructions

Program Algorithms

Application

Memory

Data compression

Compiler/Interpreter

OperatingSystem

Data Structures

Analysis

I/O

Memory hierarchy

Design

Methodologies/Tools

Process

Truth tableVenn DiagramDeMorgan’s Law

Numbers, text,audio, video, image, …

Decimal, Hexadecimal, Binary

AND, OR, NOT, XOR, NAND, NOR,etc.

Register, CacheMain Memory,Secondary Storage

Context switchProcess vs. ThreadLocks and deadlocks

Op-code, operandsInstruction set arch

Lossless v. lossyInfo entropy & Huffman code Adders, decoders,

Memory latches, ALUs, etc.

DataRepresentation

Data

Data storage

Principles

ALUs, Registers,Program Counter, Instruction Register

Network

Distributed Systems Security

Cryptography

Standards & Protocols

Inter-processCommunication

Searching, sorting,Encryption, etc.

Stacks, queues,maps, trees, graphs, …

Big-O

UML, CRC

TCP/IP, RSA, …

ConfidentialityIntegrityAuthentication…

C/S, P2PCaching

sockets

Formal models

Finite automataregex

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Central Processing Unit (CPU) Software programs consist of arithmetic and logical operations

The CPU or processor of a machine is responsible for executing these operations in hardware

Modern CPUs are implemented using tens of millions of transistors (switches)

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Central Processing Unit (CPU) CPU components:

- Arithmetic/Logic Units (ALU)- Control Unit- Registers- Cache Memory

http://www.ischool.berkeley.edu/~chuang/images/mips_r10000.jpg

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Boolean Logic

Boolean algebra = logical calculation of truth values (true/false values)

Basic boolean operators- AND- OR- XOR (exclusive-OR)- NOT

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AND, OR, XOR, and NOT:Gates and Truth Tables

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Boolean Notation

U

Operator

Symbol Example

AND * or • orA*B = A•B = A B = AB

OR + or U A+B = A U B

NOT¬ or ¯ or -

¬(A+B) = (A+B) = -(A+B)

XOR A B = AB + AB+

U

+

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Boolean Logic Relationships

A BC

D

Venn Diagram

C = A*B D = (A+B)

X+X = 1; X*X = 0 X+Y=Y+X; XY = YX X(Y+Z) = XY + XZ

DeMorgan’s Law:

- (A*B) = A + B

- (A+B) = A * B

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Exercise

Let’s solve a problem using Boolean Logic- First express the problem using Boolean expressions and/or truth table

- Then implement solution using Boolean gates

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NAND, NOR, XNOR

NAND and NOR gates easier to implement in hardware than AND and OR gates

Example: AND logic can be implemented with two NOTs and a NOR (DeMorgan’s Law)

AB =

A

B

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Gates

The Richest Man in the World

Devices that produce the outputs of Boolean operations when given the operations’ input values- Often implemented as electronic circuits called transistors

- Provide the building blocks from which computers are constructed- Gates are used to build up circuits that perform computations (e.g., addition, subtraction), or store values to be used later

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Inverter (NOT Gate)

Implements the simplest Boolean operator “NOT” using two transistors

Photolithography techniques used in fabrication of integrated circuit (IC) chips

http://www.csee.umbc.edu/~plusquel/vlsi/slides/chap3_2.html

Image and further reading at: http://www.lithoguru.com/scientist/lithobasics.html

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NAND Gate

NAND gate implemented using 4 transistors

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Integrated Circuit (IC) Chips Contain Gates & Connectors

Images from http://www.ee.ed.ac.uk/~gaa/DigilabNotes/Digilab/Components/node7.html

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Circuits for Binary AdditionHalf Adder

Images from http://www.play-hookey.com/digital/adder.html

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Circuits for Binary AdditionFull Adder

Images from http://www.play-hookey.com/digital/adder.html

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Circuits for Binary AdditionFull Adder, 4 bit output + carry

Can link up an arbitrary number of input bits

Can modify this easily to do subtraction

Images from http://www.play-hookey.com/digital/adder.html

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Arithmetic Logic Unit (ALU)Add, Subtract, and Logic Operations

http://www.seas.upenn.edu/~ee201/lab/LabALU/ALU.html

multiplexer

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CPU Operation

Bits & BytesBinary Numbers

Number Systems

Gates

Boolean Logic

Circuits

CPU Machine Instructions

Assembly Instructions

Program Algorithms

Application

Memory

Data compression

Compiler/Interpreter

OperatingSystem

Data Structures

Analysis

I/O

Memory hierarchy

Design

Methodologies/Tools

Process

Truth tableVenn DiagramDeMorgan’s Law

Numbers, text,audio, video, image, …

Decimal, Hexadecimal, Binary

AND, OR, NOT, XOR, NAND, NOR,etc.

Register, CacheMain Memory,Secondary Storage

Context switchProcess vs. ThreadLocks and deadlocks

Op-code, operandsInstruction set arch

Lossless v. lossyInfo entropy & Huffman code Adders, decoders,

Memory latches, ALUs, etc.

DataRepresentation

Data

Data storage

Principles

ALUs, Registers,Program Counter, Instruction Register

Network

Distributed Systems Security

Cryptography

Standards & Protocols

Inter-processCommunication

Searching, sorting,Encryption, etc.

Stacks, queues,maps, trees, graphs, …

Big-O

UML, CRC

TCP/IP, RSA, …

ConfidentialityIntegrityAuthentication…

C/S, P2PCaching

sockets

Formal models

Finite automataregex

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Central Processing Unit (CPU)

Software programs consist of arithmetic and logical operations

The CPU or processor of a machine is responsible for executing these operations in hardware

CPU components- Arithmetic/Logic Units (ALU)- Control Unit- Registers- Cache Memory

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Program execution Controlled by two special-purpose registers- Program counter: address of next instruction- Instruction register: current instruction

Steps performed by control unit- Fetch- Decode- Execute

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Machine language

Machine instruction: an instruction coded as a bit pattern directly recognizable by the CPU

Machine language: the set of all instructions recognized by a machine- Also known as instruction set architecture (ISA)- E.g., Intel x86, IA-64, MIPS, PowerPC, …

- Brookshear Appendix C provides an example

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Example Machine Architecture (Brookshear Appendix C)

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Machine instruction types

Data Transfer: copy data between CPU and main memory

Arithmetic/Logic: use existing data values to compute a new data value

Control: direct the execution of the program

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Parts of a machine instruction

Op-code: specifies which machine operation to execute- One per instruction

Operand: more detailed information about this operation- Number of operands varies depending on op-code

Example:

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Example: Decoding the instruction 35A7

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Example: Addition Operation

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Readings for Next Week

Read: Brookshear Chapter 5.1-5.5, 6.1

Review: Brookshear Chapter 6.2-6.5

Read: Brookshear Chapter 7.1-7.7 Read:

- http://en.wikipedia.org/wiki/Unified_Modeling_Language