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

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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 ExampleWhite 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.CS 150 Spring 2008 Lec #22: Othello Design Example - 5

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 willKeep 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 moveFlip all the discs who have been outflanked

Focus of todays 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 SystemCircuit 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 MachineFlip Current Color

NLegal Move?

Flip Current Color Legal Move?

Game Over

Current Color = White

N

YUpdate Board

Y Move selectedEnable Move

Move selected

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Square FSM Basic FunctionsStore 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 MachineState=none

k

t Se

te= b

lac

sta wh te=

Se t

sta

ite

Flip whiteState=black State=white

Flip black

Finite State Machine (Macro) per Othello Square

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Whats a Legal Move? Decided in each square Square state must be empty

Run of colorsStraight line of squares of one color bordered by a square of the other colorWhite 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 moveSquare 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); Cell is white (black); and Neighbor in direction continues or originates a white (black) run

Continues a white (black) run

Move to a square is legal if and only ifCurrent 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 RemoteBlack: this square is white all the squares in some direction are white until we hit a black Reverse black/white for Remote White

RemoteOrLocalBlack: 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 pictureNW Neighbor North Neighbor NE 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

West Neighbor

Othello Cell

East Neighbor

SW Neighbor

South Neighbor

SE Neighbor

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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 SECS 150 Spring 2008 Lec #22: Othello Design Example - 19

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 pictureNW Neighbor North Neighbor NE Neighbor

On each link:2 wires in 4 wires outLocal 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

West Neighbor

Othello Cell

East Neighbor

Global OutputsSW 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 ifCurrent Mover is white (black) Current State is empty Some neighbor continues or orginates a black (white) run

Translate into our circuitCurrent Mover is white (black) Current State is empty For some direction: neighbors remoteWhite (black)

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Computation of LegalCurrent 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

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Whats the delay? Worst case is on edge or cornerAt 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 easyOne 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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FlippingMove

Flip

How can we build a flip function?CS 150 Spring 2008 Lec