Toward a general purpose computer Example: Game of Life

Toward a general purpose computer

Example: Game of Life

Game of Life

For Each Line

For Each Cell Solve Cell

Game of Life

For Each Line

For Each Cell Solve Cell

Generation Line CellMatrix

Modularity

Generation Module Matrix Module Line Module Cell Module

Algorithm for the Generation Module

1. CurrentGen = 02. Solve for current Matrix3. CurrentGen++4. If CurrentGen < MAX_GEN

goto 2

Solve Matrix

0. j = 11. Calculate line (j)2. If j < MAX_LINE

2.1 j++2.2 goto 1.

3. STOP

Calculate Line j0. i = 0, tmp = 01. Calculate Cell i.2. If alive, set location i in tmp to alive3. If i < MAX_CELL

3.1 i++3.2 goto 1.

4. Store tmp in : even generation: i+16odd generation : i-16

CellAlive(cell index i, line index j)

0. N = Count_Neighbors(i,j-1,false)1. N = N+Count_Neighbors(i,j,true)2. N =

N+Count_Neighbors(i,j+1,false)3. If N > MIN && N < MAX 3.1 Return alive4. Return dead

Count_Neighbors(index i,line j,

center)

0. N = 0 1. If alive in location [i-1,j]: N=N+12. If not center:

2.1 If alive in location [i,j]: N=N+1

3. If alive in location [i+1,j]: N=N+14. Return N

Algorithm implementation

Algorithm

How to do? What to do?

The operation itself control

The operations in the algorithm:

Operations: Add Subtract

The operation:Defining interfaces

CountNeighbors

CellAlive

Calculate Line

Solve Matrix

Generation

Return Number of Neighbor: N

Alive: 0..010..0

Dead: 0000000

(i-1) location

Return the line

The matrix

Return

The Operation itself

Implementing instructionsModule Count_Neighbors, instruction 1, 2.1, 3

decode(i-1) = 0001000AND

Line (j) = 00010100

Result = 00010000

decode(i-1) = 0001000AND

Line (j) = 00000100

Result = 00000000

Zero – cell in location i is dead

Non Zero – cell in location i is alive

If alive in location [i-1,j]


Implementing instructionsModule Count_Neighbors, instruction 1, 2.1, 3

Alive if AND(line,decode(i-1)) is not zero

If alive in location [i-1,j]


The operations in the algorithm:

Operations: Add Subtract The logic AND + Check if zero


Small ALU (arithmetic logic unit)

Op selector

Meaning Result

00 Add Res = InputA+InputB

01 Subract Res = InputA+ NOT(InputB)+1

10 AND Res = AND(InputA,InputB)

11 Decode Res = decode(InputA)


Small ALU

MUX

S0S1S2

Adder

Adder

1

ReductionOR

Zero Result

Input A Input B

Decode

StatusBit


Small ALU

StatusBit


ALU

isZero

Op

InputBInputA

Implementation of AND(line,decode(i+1))

Reg1

Reg2

Reg3

Regn


Reg1

Reg2

Reg3

Regn

ReadA

ReadB

1

2

Connected like MUX 1


Reg1

Reg2

Reg3

Regn

ReadA

ReadB

1

2

Decoder

Enable Write

Write Address

Write Data


Registers

Data 1

Data 2

Data 1 Address

Data 2 Address

WriteAddress

Write Data

Write

Variables of the algorithmCount_Neighbors

Variable Meaning AddressCurrentLine Hold the current

line0

I The current index 1

N The Neighbor 2

Tmp Temporary space 3

Constant 1 Constant 1 5

ControlVariable A flag to determine if the operation should

be performed

6

Center Is it the center 7

Variables of the algorithmCount_Neighbors

Variable Meaning AddressCurrentLine Hold the current

line0

I The current index 1

N The Neighbor 2

Tmp Temporary space 3

Constant 1 Constant 1 5

ControlVariable A flag to determine if the operation should

be performed

6

Center Is it the center 7

Register/ALU circuit

Registers

Data 1 Address

Data 2 Address

WriteAddress

Write

ALU

Op

Extend 1to 16

MU

X R0R1

ExternalInput

0

1

2

Control Algorithm is zero[AND(line,decode(i+1))]

If alive in location [i+1,j]: N=N+1

Algorithm instruction

Instruction a. Tmp = is zero[AND(Currentline,decode(i+1))]

b. If controlVariable=0000001: N=N+1


Control Algorithm is zero[AND(line,decode(i-1))]

Tmp = is zero[AND(line,decode(i-1))]Instruction


t0. Tmp = i-1t1. Tmp = decode(Tmp)t2. controlVariable = is zero[AND(CurrentLine, Tmp)]

Micro-Instruction

Micro instruction implementation

t0. Data 1 Address = 1Data 2 Address = 5WriteAddress = 3

Write = 1 Op = 01R0R1 = 01

Micro-Instruction


a. Tmp = i+1b. Tmp = decode(Tmp)c. controlVariable = is zero[AND(CurrentLine, Tmp)]

Subtract

i1

tmp

The result of the ALU



Write = 1 Op = 11R0R1 = 01



Decode

tmpIrrelevant

tmp

The result of the ALU

Micro-Instruction



Write = 1 Op = 10R0R1 = 00



And

Line in register itmpcontrolVariable

The zero status bit

Micro-Instruction

Instruction Hierarchy

Instruction

Micro-Instruction

Micro-Instruction

Micro-Instruction

Micro-Instruction

Instruction

Algorithmic Instruction


Instruction Hierarchy

Instruction

t0: Micro-Instruction

tn: Micro-Instruction

t0: Micro-Instruction

tn: Micro-Instruction

Instruction

Each micro instruction = 1 cycle

Timing Variable

s

Timing variables (example with 4 time variables)

CP

t0

t1

t2

t3

One instruction

Generating Timing variablesexample with 16 timing variables

CP Register 4bits

Adder

1Decoder

t0

t15

Control of Count_Neighbor

1. N=0

3. i-1 alive?

4. N=N+1

5. Is Center?

6. i alive

7. N=N+1

Yes

No

No

Yes

8. i+1 alive

Yes

No

9. N=N+1

end

Yes

No


0000

0001

0010

0011

0100

0101

0110

0111

1000

1. N=0

3. i-1 alive?

4. N=N+1

5. Is Center?

6. i alive

7. N=N+1

Yes

No

No

Yes

8. i+1 alive

Yes

No

9. N=N+1

end

Yes

No


0000

0001

0010

0011

0100

0101

0110

0111

1000

1. N=0

3. i-1 alive?

4. N=N+1

5. Is Center?

6. i alive

7. N=N+1

Yes

No

No

Yes

8. i+1 alive

Yes

No

9. N=N+1

end

Yes

No

Putting it all together:implementing what to do with ROM

Current State

Timing CV C D1 D2 WA W Op R0R1t0 t1 t2 t3

ROM Input ROM Output

The current state(4 bits) The current timing variable

(1 bits)

Control variable (16bits)

CenterRegister 7 (16bits)

Putting it all together: implementing what to do with ROM

Data 1 Address


Data 2 Address Write-Data MUX control

WriteAddress

WriteALU Operation

Current State

Timing CV C D1 D2 WA

W Op R0R1

t0 t1 t2 t3

Putting it all together: implementing what to do with ROMROM Input ROM Output

Current State

Timing CV C D1 D2 WA W Op R0R1

t0 t1 t2 t3

0001 1 0 0 0 1 5 3 1 01 01

0001 0 1 0 0 3 0 4 1 11 01

0001 0 0 1 0 0 3 6 1 10 00

0010 0 0 0 1 0 0 0 0 000 01t0. Tmp = i+1t1. Tmp = decode(Tmp)t2. controlVariable = is

zero[AND(CurrentLine, Tmp)]t3. do nothing


Current State


t0 t1 t2 t3

0001 1 0 0 0 1 5 3 1 00 01

0001 0 1 0 0 3 0 4 1 11 01

0001 0 0 1 0 0 3 6 1 10 00




Current State


t0 t1 t2 t3

0001 1 0 0 0 1 5 3 1 00 01

0001 0 1 0 0 3 0 4 1 11 01

0001 0 0 1 0 0 3 6 1 10 00




Current State


t0 t1 t2 t3

0001 1 0 0 0 1 5 3 1 00 01

0001 0 1 0 0 3 0 4 1 11 01

0001 0 0 1 0 0 3 6 1 10 00




0000

0001

0010

0011

0100

0101

0110

0111

1000

1. N=0

3. i-1 alive?

4. N=N+1

5. Is Center?

6. i alive

7. N=N+1

Yes

No

No

Yes

8. i+1 alive

Yes

No

9. N=N+1

end

Yes

No

t0. Set Current State 0001t1. Set Current State 0001t2. Set Current State 0001t3. If ControlVariable=1

Set Current State 0010t3. If ControlVariable=0

Set Current State 0011

Current State = 0001

Putting it all together:implmenting control with ROM


Current State

Timing CV C NextState

t0 t1 t2 t3

0001 1 0 0 0 0001

0001 0 1 0 0 0001

0001 0 0 1 0 0001

0001 0 0 0 1 1 0010

0001 0 0 0 1 0 0011

Here is the branch.

ROM

Timing Variable CurrentState

Registers

ALUExtend 1

to 16

MU

XR0R1

Resultzerobit

Op

D1D2

WA

Write

WriteData

Next State

Current State

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Toward a general purpose computer Example: Game of Life