DIGITAL SYSTEMS 2004 Rudolf Tracht and A.J. Han Vinck

Some definitions: Information: –Knowledge that can be used (messages, measurements) Information science: –the science concerned with gathering and manipulating and storing and retrieving and classifying recorded information Information systems: –The entire infrastructure, organization, personnel, and components for the collection, processing, storage, transmission, display, dissemination, and disposition of information. [INFOSEC-99] Information theory: –a statistical theory dealing with the limits and efficiency of information processing Computer science: –The discipline that is concerned with methods and techniques relating to data processing performed by automatic means.

Content of course Components and design techniques for –digital inputs/outputs and internal values are from a finite set –For instance binary, i.e. 0 or 1 and –time-discrete systems changes in the system are controlled by a global clock

from analog to digital/time discrete Analog digital ( 1, 3, 1, 2,...) CLOCK: time V(t) time discrete signal

How accurate/fast should we sample? not accurate enough: – introduces distortion! not fast enough: –Signal theory explains how fast we should sample for unique reconstruction CD samples at 44.1 kHz, every sample has 16 bits very accurate/too fast: –too many bits –not necessary Distortion determined by perception!

from digital/time discrete to analog digital ( 1, 3, 1, 2,...) analog time Example! CLOCK:

Binary representation Shannon uses: Binary Information digiTS (BITS) 0 or 1 n bits specify M = 2 n different values OR M values specified by n =  log 2 M  bits Ex: M = 11,  n = 4

Logic levels Logic levels for typical logic circuits 5.0 v logic 1 (High) 3.5 v undefined 1.5 v logic 0 (Low) 0.0 v

Digital waveforms Ideal pulses high rising edge falling edge –Positive going negative going low Nonideal pulse 90% non linearities 50% 10% rise time fall time

Periodic/nonperiodic pulses Periodic: repeats itself at fixed interval (period T) period Tfrequency : = 1/T (Hertz) nonperiodic duty cycle: (t w /T) 100% T t w

the binary world easy to process binary data –we know only 0 or 1, reproducibility of results easy to store binary data –fast disk and CD-ROM storage devices, cheap and small –Memory stick easy to transmit and protect –data protection well developed; easier than analog easy to describe mathematically –we use discrete mathematics

Waveform carrying information Binary information is transmitted as High or Low during one cycle of the clock clock bit time bit sequence represented by the above waveform

Data transfer Serial Parallel

EXAMPLES: text:represent every symbol with 8 bit  storage: 8 * (500 pages) * 1000 symbols = 4 Mbit  compression possible to 1 Mbit (1:4) speech: sampling speed 8000 samples/sec; accuracy 8 bits/sample;  needed transmission speed 64 kbit/s  compression possible to 4.8 kbit/s (1:10) CD music: sampling speed 44.1 k samples/sec; accuracy 16 bits/sample  needed storage capacity for one hour stereo: 5 Gbit  1250 books  compression possible to 4 bits/sample ( 1:4 ) digital pictures: 300 x 400 pixels x 3 colors x 8 bit/sample  2.9 Mbit/picture; for 25 images/second we need 75 Mbit/s 2 hour pictures need 540 Gbit  books  compression needed (1:100) DVD has 4.7 Gbyte storage capacity

What is system design? –Solution to a given specification of a problem –choose appropriate components –meet criteria for size, cost, power, beauty, etc. –improve on one at the expense of the others

Example Digital System Low power operation comes at the expense of: lower speed higher cost Designed to minimize power. Single battery must last for years.

Example Digital System Digital Computer –designed to maximize performance. "Optimized for speed"

Cont‘d Cache: high-speed storage mechanismALU: Arithmetic Logic Unit

Hierarchy in design Top-Down: start at root and work down by successive refinement Bottom-Up: start at leaves & put pieces together to build up the design

What is digital hardware? Collection of devices that sense and/or control wires carrying a digital value (i.e., a physical quantity interpreted as a “0” or “1”) –e.g., digital logic where voltage 3.5V is a “1” –Computers are digital hardware because at their most basic level they can distinguish between just two values, 0 and 1, or off and on. –e.g., orientation of magnetization signifies a “0” or a “1”

Components (combinational) Combinational –No memory, output is just a function of actual input Ex: F = f(a,b) –Basic Logic computation devices two wires both “1” - make another be “1” AND at least one of two wires “1” - make another be “1” OR a wire “1” - then make another be “0” NOT and or not

Logic functions Comparison A A > B high if true, low if false 2 binary numbers in A = B BA < B ex: A = 2, B = 5  (0, 0, 1) Addition (011) A sum A + B (010) (110) Bex: A = 3, B = 6, C = 1  10 = (carry out = 1) C carry incarry out (overflow) (1)

multiplexing Multiplex select one out of 4 inputs A B Coutput line D

demultiplexing demultiplex A inB C D Select output line: one out of 4

Storage (sequential machine) Flip flop: stores a bit (1 or 0): The output is High for 1, Low for 0 Action: when clock goes high, –memory content = input –Output = memory content inputoutput clock input clock output

Registers (sequential) Register: (many vatiations) –Consists of Flip-Flops to store information –Can be used to shift information in or out serial in serial out parallel in serial out clock Signal selects parallel in or serial out low

More Logic functions Subtraction Multiplication (slow) Division (slow)ALU Addition Logic bit operations

Some history Aristotle 322 BC formulation of logic 1850: George Boole invents Boolean algebra –Permits manipulation of logic statements using mathematics 1938: Claude Shannon links Boolean algebra to switches (relays) 1945: John von Neumann develops first stored program computer (vacuum tubes) 1946: ENIAC--world’s first all electronic computer (18,000 vacuum tubes) –Several hundred multiplications per minute 1947: Shockley, Brittain, and Bardeen invent the transistor –replaces vacuum tubes –enable integration of multiple devices into one package

Digital Communication 1948SHANNON: –start of digital communication source- channel- security- 1970start of satellite communciation 1974Glasfiber communication 1976Ungerböck digital line modems 1980CD Philips-Sony 1980ALOHA, start of networking 1995GSM 2000xDSL

Why DS ? Obvious reason –Implementation basis for all modern computing/communication devices Building large things from small components Provide another view Faster, cheaper, more efficient etc. More reasons –Inherent parallelism in hardware –In addition to software design –Embedded complexity (p x q)