Computer Fundamentals

ELEC 330

Digital Systems Engineering

Dr. Ron Hayne

330_01 2

Review of Number Systems

Number Systems (Conversions) Binary Octal Hex

Negative Numbers Two’s Complement Sign Extension

Arithmetic Addition (Subtraction)

Codes BCD ASCII

330_01 3

Positional Number Systems

1

22

11

00

11

210110

10101010

10510210310225.23

p

ni

ii rdD

ddddD

330_01 4

Binary

10

210122

22

11

00

11

22

1

25.5

25.015.00112041

212021202101.101

22222

2

bbbbbB

bBp

ni

ii

330_01 5

Number Systems

330_01 6

Octal and Hexadecimal

16

22

8

22

4.2

]0100].[1100][0010[01.101100

2.54

]010].[100][101[01.101100

C

330_01 7

Octal and Hexadecimal

10

10116

10

1018

10

2

25.44

16416121624.2

25.44

8284852.54

25.44

25.0483201.101100

C

330_01 8

Conversions

13.37510 = ?2

132

6 R 12

3 R 02

1 R 12

0 R 1 (MSB)

0.375 x 2 = 0.75

0.75 x 2 = 1.5

0.5 x 2 = 1.0 (LSB)

13.37510 = 1101.0112

330_01 9

Binary Addition (Full Adder)

CIN X Y COUT S

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

330_01 10

4-bit Addition Example

X+ Y

S

0+

1001100

0

1

0

0

1

1

0

0

0

2+ 3

5

330_01 11

Negative Numbers

330_01 12

Two’s Complement

MSB serves as sign bit (fixed-width) 0 => positive 1 => negative

Negation Operation Complement all bits Add 1

Alternate Negation Operation Starting from right to left

Copy up to and including the first 1 Complement the rest

330_01 13

2 = -610

2 = +610

Two’s Complement (4-bit)

+610 = 01102

1001 +1

10102 = -610

1010

0101 +1

01102 = +610

1001

330_01 14

Two’s Complement Arithmetic

Examples (4-bit)

3 - 6 = -3

-4 - 5 = ?

330_01 15

Overflow

Operation produces a result that exceeds the number system

Example (4-bits) Range -8 to +7

Detection Rule Overflow occurs if the addends’ signs are the

same, but the sum’s sign is different from the addends’

330_01 16

Sign Extension

Converting a Two’s Complement Number to an Equivalent with More Bits 4-bit to 8-bit 8-bit to 16-bit

Reproduce the Sign Bit +6 = 01104-bit = 000001108-bit

-6 = 10104-bit = 111110108-bit

330_01 17

Binary-Coded Decimal (BCD)

Encodes digits 0 thru 9 4-bit unsigned binary

0000 thru 1001

6 unused code words 1010 thru 1111

Packed BCD 8-bit byte 2 BCD digits

330_01 18

BCD Arithmetic

Correction made if result exceeds 1001 Add 6 Produces carry

36 0011 0110+ 27 + 0010 0111 63 0101 1101 + 0000 0110 0110 0011

330_01 19

Character Codes

ASCII (7-bits) American Standard Code for Information Interchange

330_01 20

Summary

Number Systems (Conversions) Binary Octal Hex

Negative Numbers Two’s Complement Sign Extension

Arithmetic Addition (Subtraction)

Codes BCD ASCII

330_01 21

Digital Systems

Logic Gates Building Blocks

Combinational Sequential Memory

Examples Synchronous Serial Communications Instruction-controlled Information Processor

330_01 22

Logic Gates

X Y X Y

X_

330_01 23

More Logic Gates

X Y_____

X Y_____

330_01 24

Binary Decoder (n-to-2n)

Activates exactly one of 2n outputs based on an n-bit input value

330_01 25

Multiplexer

Digital Switch Selects 1 of n sources Based on s control lines n = 2s Sources b bits wide

330_01 26

Arithmetic Logic Unit (ALU)

330_01 27

Edge-Triggered D Flip-Flop

330_01 28

4-bit Binary Counter

Synchronous Active-low Load Active-low Clear

Two Enables ENP (parallel) ENT

Ripple Carry Out RCO (ENT) Cascading

330_01 29

Universal Shift Register

330_01 30

Register Notation

Serial Transfer

Parallel Transfer

Register Contents

RC Logical Shift Left0

R

1 0 1 1 0 1 0 1 B 5

330_01 31

Buses and Transfer Gates

Transfer

Transfer

Transfer

88

330_01 32

Memory Organization

Dimensions n-bit words k-bit address

Operations Read, Load, Fetch Write, Store

Memory

first word

next word

last word

n bitsAddress

0

1

2k-1

.

.

.

330_01 33

Memory

Memory Signals Memory Model

Mem

Address

Data

Read/Write

Clock

0000

C329 B6

C23A C1

C23B 33

FFFF 22

330_01 34

Example Digital System

Synchronous Serial Communications

Parallel Register Parallel Register

Shift RegisterShift Register

ControlUnit

CountF

Slave DeviceMaster Device

Transmit

Receive

Clock

330_01 35

Example Digital System

Instruction-controlled Information Processor Arithmetic Logic Unit Registers Transfer Gates Input Port Output Port Control Unit

ALU

A B

OU

T

Processor

XIN

LA LB

XA XB

LOUT

C0C1

ControlUnit

C0C1

XAXBLALB

XINLOUT

Clock

OUT

IN

C0 C1 Operation

00 IN1 + IN2 OUT

01 IN1 + IN2 + 1 OUT

10 IN1 + IN2 OUT

11 IN1 + IN2 + 1 OUT

330_01 37

System Operation

IN - B OUT

Control Signals

Step RTL XIN LA LB XA XB C0 C1 LOUT

1 IN A 1 1 0 0 0 0 0 0

2 A - B A 0 1 0 1 1 1 1 0

3 A OUT X 0 0 X X X X 1

330_01 38

Summary

Logic Gates Building Blocks

Combinational Sequential Memory

Examples Synchronous Serial Communications Instruction-controlled Information Processor

330_01 39

Processors

Stored Program Processors General-Purpose Computers Microprocessors Microcomputers Microcontrollers

330_01 40

Building Blocks

Clock Processor

ALU Registers

Control Unit Memory Input/Output

330_01 41

Stored Program Processor

Input/Output

ProcessorControl

Unit

In

Out

Data

Memory

Data

Control

Instruction

Control/StatusClock

330_01 42

Memory

Instructions Program Software

Data Load Store

Memory Model

0000

C329 B6

C23A C1

C23B 33

FFFF 22

330_01 43

Instruction Operation

Fetch Phase PC

Program Counter IR

Instruction Register

M[PC] IR PC + 1 PC

Execute Phase Instruction dependent

Example: Load Accumulator A LDAA $34

M[34] A

330_01 44

General-Purpose Computer

Arithmetic Operations Logical Operations Load and Store Operations Testing and Branching Input and Output

330_01 45

Computer Architecture

Princeton von Neumann

Memory holds both instructions and data

Input/Output

ProcessorControl

Unit

In

Out

Data

Memory

Data

Control

Instruction

Control/StatusClock

330_01 46

Computer Architecture

Harvard Separate instruction

and data memories

Input/Output

ProcessorControl

Unit

In

Out

Data

DataMemory

Data

Control

Instruction

Control/StatusClock

InstructionMemory

330_01 47

Microprocessor/Microcomputer

Microprocessor Single Integrated Circuit (IC) Processor and Control Unit

Microcomputer Single Printed Circuit Board

Interconnection of multiple ICs Microprocessor, Memory, I/O, Clock

Microcontroller Single-Chip Microcomputer

330_01 48

Microcomputer/Microcontroller

Input/Output

ProcessorControl

Unit

Memory

ClockMicrocomputer/Microcontroller

Microprocessor

330_01 49

Embedded Control Systems

Microcomputer inside a device that is not called a computer Satellite TV Receivers Microwave Ovens Programmable Thermostats Automobiles Robotics

330_01 50

Personal Computers

PC Collection of components that contain many

microcomputersCentral Microcomputer (CPU)Keyboard ControllerDisk Drive InterfaceDisplay Monitor InterfacePrinter

330_01 51

Summary

Stored Program Processors General-Purpose Computers Microprocessors Microcomputers Microcontrollers