A Game of Othello
 Othello: popular board game (often known as Reversi)
 8x8 board, black and white tokens
 Today, we will use it as a design example
CS 150 – Spring 2008 – Lec #22: Othello Design Example - 1
Othello: Rules and Game Play
 The object of the game is to have the majority
of your colour discs on the board at the end of
the game
 Rules
 Black places two black discs and White places
two white discs as shown in here. The game
always begins with this setup.
 A move consists of "outflanking" your
opponent's disc(s), then flipping the outflanked
disc(s) to your colour.
 To outflank means to place a disc on the board
so that your opponent's row (or rows) of disc(s)
is bordered at each end by a disc of your colour.
(A "row" may be made up of one or more discs).
 Here's one example: White disc A was already in
place on the board. The placement of white disc
B outflanks the row of three black discs.
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Outflanking Example
White disc A was already in place on the board. The
placement of white disc B outflanks the row of three
black discs.
White flips the outflanked discs and now the row
looks like this:
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Rules
 Black always moves first.
 If on your turn you cannot outflank and flip at least one opposing
disc, your turn is forfeited and your opponent moves again.
However, if a move is available to you, you may not forfeit your
turn.
 A disc may outflank any number of discs in one or more rows in
any number of directions at the same time - horizontally,
vertically or diagonally.
 You may not skip over your own color disc to outflank an opposing
disc.
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Rules
 Discs may only be outflanked as a direct result of a move and
must fall in the direct line of the disc placed down.
 All discs outflanked in any one move must be flipped,
even if it is to the player's advantage not to flip them
at all.
 Once a disc is placed on a square, it can never be
moved to another square later in the game.
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Rules
 When it is no longer possible for either player to
move, the game is over. Discs are counted and the
player with the majority of his or her colour discs on
the board is the winner.
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Our Design Problem
 Design an Othello Board and Gamekeeper.
 The gamekeeper will
Keep track of the score and state of the board
Indicate whose move it is
Indicate where legal moves can be made
Accept and make a legal move
Flip all the discs who have been outflanked
 Focus of today’s lecture
Game engine and logic alone
We will assume
Display device for an 8x8 board
Input device which tells us where to move on an 8x8 board
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Global Picture of Our System
Circuit in Each Square to:
1. Keep State of the Square
2. Compute whether move in
square is legal
Game Controller
1.
Global Game
State
2. Orchestrates
individual
move logic
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Game Controller State Machine
Flip
Current
Color
N
Legal
Move?
Current
Color =
White
Game
Over
Flip
Current
Color
Legal
Move?
Y
N
Y
Update
Board
Move
selected
Enable
Move
Move
selected’
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Square FSM
 Basic Functions
Store state of square (Empty, White, Black)
Report when move is legal
Report when user moves into square
Update state of square in response to a move
Current
Color
Move
Enabled
Square
Move
Selected
Legal
Move
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Square Finite State Machine
sta
lac
te=
b
t
Se
k
State=none
ite
Se
t
sta
wh
te=
Flip white
State=black
State=white
Flip black
Finite State Machine
(Macro) per Othello
Square
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What’s a Legal Move?
 Decided in each square
 Square state must be empty
 “Run” of colors
Straight line of squares of one color bordered by a square of
the other color
White run: line of white squares terminated by black square
Black run: line of black squares terminated by white square
Current run: line of squares of current color terminated by
square of other color
 Legal move
Square is empty and neighbor square is part of current run
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Key Consideration for Cell
 Is it on a “run” in any direction?
Originates a white (black) run:
Cell is white (black); and
Neighbor in direction is black (white);
Continues a white (black) run
Cell is white (black); and
Neighbor in direction continues or originates a white (black) run
 Move to a square is legal if and only if
Current Mover is white (black)
Current State is empty
Some neighbor continues or orginates a black (white) run
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Originating and Continuing a Run
Begins a black run
Continues a white run
Begins a white run
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Legal Moves
Legal to move white
Legal to move black
How do we build a circuit to pick this up?
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Two Functions Per Color and direction
 Remote
Black: this square is white
all the squares in some direction are white until we hit a black
Reverse black/white for Remote White
 RemoteOrLocal
Black: this square is black OR remoteBlack is true for this
square
 Note that if a square is empty both remote and
remoteOrLocal are false.
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Originating and Continuing a Run
remoteWhiteEast
remoteOrLocalBlack (all
directions)
remoteOrLocalBlack East
remoteOrLocalWhite (all
directions)
remoteOrLocalBlackWest
remoteBlackWest
remoteOrLocalWhite (all directions)
remoteOrLocalBlackWest
remoteBlackWest
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Cell circuit picture
NW
Neighbor
North
Neighbor
NE
Neighbor
West
Neighbor
Othello
Cell
East
Neighbor
SW
Neighbor
South
Neighbor
SE
Neighbor
Local Inputs and Outputs
(Connections to Adjoining cells)
Cell has remote black
Cell has remote white
Cell has localOrRemote black
Cell has localOrRemote white
Flip black
Flip white
Global Outputs
Cell color (black, white, none)
Legal to move to current color
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RemoteBlack (Continue White Run)
Cell Color = white
SE Neighbor
localOrRemote black
Remote black to (NW
neighbor)
Computation of remote (8x2, one
to each neighbor x one per color)
White run
to NW
White run
from SE
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RemoteOrLocal black (on white run or
neighbor can start white run)
Cell Color = black
remoteBlack
local orRemoteblack to
(NW neighbor)
Computation of localOrRemote
(8x2, one to each neighbor x one
per color)
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Cell circuit picture
On each link:
2 wires in
4 wires out
NW
Neighbor
West
Neighbor
North
Neighbor
Othello
Cell
NE
Neighbor
East
Neighbor
Local Inputs and Outputs
(Connections to Adjoining cells)
Cell has remote black
Cell has remote white
Cell has localOrRemote black
Cell has localOrRemote white
Flip black
Flip white
Global Outputs
SW
Neighbor
South
Neighbor
SE
Neighbor
Cell color (black, white, none)
Legal to move to current color
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Legal Move
 Move to a square is legal if and only if
Current Mover is white (black)
Current State is empty
Some neighbor continues or orginates a black (white) run
 Translate into our circuit
Current Mover is white (black)
Current State is empty
For some direction: neighbor’s remoteWhite (black)
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Computation of Legal
Current Mover = black
NW remote black
Current Mover = white
NW remote white
8 inputs,
one per
neighbor
Cell color
= none
legal
Computation of legal
Computation from one
direction
Replicate here from
each neighbor
CS 150 – Spring 2008 – Lec #22: Othello Design Example - 23
What’s the delay?
 Worst case is on edge or corner
At most 7 AND or OR gates on remote chain
Computation of legal is ~6 gates (figure 3 gate delays for 8input OR)
Total delay is 13 gates
 Note (Synchronous Mealy) we want to latch the
output of legal!
 What about the edges and corners? More later…
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How much logic in a cell?
 8x2 AND gates for remote = 16
 8x2 OR gates for localOrRemote = 16
 3 gates for leaf of legal computation (8 leaves), so
8x3 = 24
 7 OR gates + 1 AND gate for rest of legal computation
 Total 64 gates/cell (so far)
 Also need at least 2 latches for color + one for legal
 More logic to come
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Doing The Move
 This is easy
One external select (keyed by button or multiplexer from
joystick – not our problem today)
Select & legal (previously computed)
 Still have to flip…
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Flipping
Move
Flip
How can we build a flip function?
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Flipping
Move = black
RemoteBlackNorth =
True
RemoteBlackEast =
True
Square selected
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Key
 Mover sends out a flip signal, with color and direction,
to each neighbor
8x2 wires
 Flip black if
Flip black signal from one direction (SE); and
Color is white; and
remoteBlack is true in other direction (NW)
FlipBlackNW = [FlipBlackFromSE AND Color=white AND
RemoteBlackNW
Send FlipBlackNW out to NW neighbor
OR all FlipBackDirections to get Direction
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Flip Calculation
SE Flip black
NW Remote black
Cell color = white
Flip black to
NW Neighbor
Move
Cell mover = black
Computation of flip (8x2, one per
neighbor x one per color)
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Computation of Next Cell State
Current Mover=black
Move
Flip black to
each
neighbor
Next state = black (repeat for white)
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Cell circuit picture
On each link:
4 wires in
6 wires out
NW
Neighbor
West
Neighbor
North
Neighbor
Othello
Cell
NE
Neighbor
East
Neighbor
Local Inputs and Outputs
(Connections to Adjoining cells)
Cell has remote black
Cell has remote white
Cell has localOrRemote black
Cell has localOrRemote white
Flip black
Flip white
Global Outputs
SW
Neighbor
South
Neighbor
SE
Neighbor
Cell color (black, white, none)
Legal to move to current color
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Gate Delay Calculation for Clip
 7x2 gates to propagate = 14 gate delays
 But need to consider the remote chain!
Adds another 7 delays (from slide 24)
 3 gate delays through 8-way OR + 1 gate delay to
comput next state
 Worst-case is 25 gate delays
 Can reduce to 18 by latching remote signals computed
in legal-move phase
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How Many Gates
 2 gates/direction-color x 2 colors x 8 directions = 32
gates
 2 gates for current move (one black, one white)
 8 gates/color for upper end of next-state tree = 16
 Total 50 gates
 Add to 64 from slide 25
 Total 114 gates/cell
 64 cells = 7296 gates for design
 But what about the corners and edges?
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Two choices
 Cell design assumes neighbors in all directions
Note true at edges and corners
 One: special-case cells on the edge
Now have 9 different types of cell!
 1/49 cells in center of board (type 1) – cell we’ve designed
4/7 cells each on each edge (types 2-5)
4/7 cells each for each corner (types 6-9)
Note each specialty type is simpler than general case, but…
9 cell types to design! 
 Two: Surround the board with shadow squares
Less efficient, but much simpler
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Revised Board
Shadow Cells
Normal Cells
we’ve designed
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Shadow Cells
 Always empty (no next-state logic)
 Can’t be selected
 localOrRemote, local = false for all colors and
directions
 Just a small collection of 6 wires connected to ground
 Key advantage: only two cell types, one trivial
 Disadvantage: lose a little efficiency from
specialization of edge, corner cells
Always worth it! Let a synthesizer optimize away the
constants
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Timing Diagram for Each Move
Set Current Mover
Latch Legal Moves,
Remote Values
Select Square
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Update Current
State of All
Squares
Logic for controller
Read Move
From
Controller
No
Legal
Mo v e
Make No
Legal Move
Controller
Transition
l
ga
L e ve s
Mo
N
o
M Leg
ov a
e l
Start
Move
is
Legal
Update
Board
Make Legal
Move
Controller
Transition
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Game Control Logic
Move white
Move=black
Move=white
Move black
No
legal
Move
Move=black
(no white
move)
Move=white
(no black
move)
l
ga
le
o ve
N mo
No
m leg
ov al
e
Move
White
No
legal
move
Move
black
Game Over
Othello Game Controller
FSM
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Key Steps to Making the Design Work
 Software implementation first!
 I did it in Smalltalk
 Tastes Differ, but…
 OO programming model tends to fit circuits well
 Map each object onto a circuit
Variables tend to map to latches
Functions tend to map to logic circuits
 Unit test, unit test, unit test!
 Design test circuits for each component
 Synthesize test circuits as part of the design
 Audit, audit, audit!
 Pin out internal state where possible
 E.g., Legal should be displayed visually
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Timing Bugs
 Nastiest, hardest to catch
 Two common examples: Read-Before-Wirte and
Write-Before-Read
 Read-Before-Write
Reader reads sequential value before writer has updated it
Acts on old value
E.G. no legal move but controller sees legal move from
previous value
 Write-Before-Read
Writer writes before old value has been acted on
Reader doesn’t act on value
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Two Solution
 Dirty/Clean bits
Writer sets dirty bit, reader cleans it when read
Writer checks dirty bits clean before writing, reader checks
set before reading
Error raised if condition not met
 FIFO Queues
Writer writes, reader reads
Decouples send/receive asymmetries by a cycle or so
Can become event-driven: Reader only reads when new value
Still have to check overflow, etc
Automatically implemented in V++
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