State Machines for Kids A Learning Tool/Toy

for Middle School age students

Lee Felsenstein

Fonly Institute2460 Park Blvd. #1Palo Alto, CA 94306(650)814-0427

lee@fonlyinstitute.com

Steinmetz' lectures #1 and #2

Charles Proteus Steinmetz founded the modern field of electrical engineering in the

US ca. 1895

Steinmetz' lectures #1 and #2

Charles Proteus Steinmetz founded the modern field of electrical engineering in the

US ca. 1895

He delivered a series of three lectures on general electrical engineering which were published.

Steinmetz' lectures #1 and #2

Charles Proteus Steinmetz founded the modern field of electrical engineering in the

US ca. 1895

He delivered a series of three lectures on general electrical engineering which were published.

The third lecture was republished in the 1950's – the editor omitted the first two because the contents had become “general knowledge” by that time

Our goal is to develop tools that

allow the design of state machines to

become “general knowledge” -

information commonly absorbed

by the age of 13.

Disappearance of the Bit

It is possible to receive a degree in Computer Science without encountering the concept

of the bit.

“Increasingly one must fight to include the bit in the CS curriculum' (comment by D. E. Knuth in private discussion).

Learning Toy Characteristics

People learn through play though most adults cannot admit that.

Most learning toys are physical tactile input visual or aural output easily presentable to others as reinforcement

Software is not well suited as a learning toy virtual, not easily displayed

SMLD Design Goals

Reasonable cost purchased by parent for child long life time

Immediate response and reinforcement take an action, see the response at once pushbutton clocking

Capable of wide range of configurations Interconnectable and interoperable

SMLD operating goals Require symbolic logic representation for more

than trivial results origin of software simple syntax for Boolean and sequential

operations Offer rapid reinforcement Encourage group learning Permit individual learning Support creation of meaningful tools

My first PDP-8

SMLD operating goals Require symbolic logic representation for more

than trivial results Origin of software Simple syntax for Boolean and sequential

operations Offer rapid reinforcement Encourage group learning Permit individual learning Support creation of meaningful tools

My first PDP-8

Registered State Machine 8 latches

D type – common clock D input is OR of 8 terms Terms are ANDs of inputs and outputs

upright and inverted AND functions defined by diodes inserted at

matrix crosspoints tweezer programming

LEDs indicate latch output and term states

Pedagogy Understand logic functions

NOT (output opposite of input) OR (output if ANY input active) AND (output if ALL inputs active)

Understand latch (sequential) function Output dependent on clock occurrence Output independent of input at all other times

Understand symbolic representation of logic ! (inversion), & (OR), # (AND), : (sequentiality) Latch equation Q := D

Pedagogy, continued

Each step illustrated with interactive trials Quick progress to first accomplishment

toggle operation Q := !Q push the button, watch the LED change none of your friends can do this! now, make all the LEDs do it!

Try any variation – it can't be damaged

The Matrix 8 rows of 33 holes – 32 input columns per row

8 inputs + 8 inverse (INn, !INn) 8 register outputs + 8 inverse (Qn, !Qn) Select column by MELF diode in hole

Selected terms are ANDed together All rows are ORed to form input to register

D

CLK

Q

!Q

ORA

B

INB

& & & & & && & & & & &

Q

!Q

Connect a diode at a & point to include that signal in an AND function

PU

PU

PU = resistive pull-up

!INB

!INA

LATCH

INA

Q

SMLD ELEMENTAL LOGIC BLOCK SCHEMATIC

SMLD Product – Register Board PCB 4” x 8” 8 LEDs on front edge – output status 2 pushbutton switches – Clock, Reset 8 card edge connectors for matrix boards 32-pin Eurocard connector at rear edge Unregulated DC power input jack DIP switch selects combinatorial vs. registered

SMLD Matrix Board 8 daughter cards – one per bit – 1.75” H x 4” L Top removes with 1/4 T fasteners Mini-MELF diodes placed in matrix holes on

block Grooves allow tweezer access

8 LEDs at edge display state of terms Conductive gaskets absorb component

variations

Exercises

Make a bit toggle with the clock no Boolean logic required

Decode a binary number (term LEDs - AND) OR of terms to latch Two-bit counter (modulo 4 – uses toggle) Two-bit counter (modulo 3) Ring counter (walk 1 bit down 8 latches) Johnson counter (fill 8 bits, then empty)

8-bit State Machine 256 states - Moore type Logic level outputs can drive simple effectors

Solenoids – high current requires driver transistor

Robot actions Anything using digital control inputs

Switch inputs Photosensors, keypads, joysticks, analog

comparators (with hysteresis) External clocks – up to 1 MHz

Multi-card Operation

Clock and Reset can be directly driven from Eurocard connector

8 outputs (Q0:7) 8 inputs (IN0:7) Clock (CLK) – max. rate ~1MHz Reset (RST)

With a memory board, working minicomputers (PDP-8/S e.g.) can be built from about 20 boards.

“How is this different from a microprocessor?

Tactile/visual/experimental tool for understanding how bits work

Mental models are very small and easy to understand

Building block for computers Very short path to reinforcement

Future

SMLDs work together, so kids can form larger projects together

~20 kids with SMLDs and a memory board can build a PDP-8/S minicomputer

Peripherals - sensors and effectors printer communications buildable and understandable by kids 11-14

Status

SMLD board set designed and in layout stages 2-bit prototype (exhibited) has been tried in 4

event with 10 – 14 year old kids 14 pages of courseware written and edited

based on proto trial Seeking partners in bringing SMLD to market