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Toward a general purpose computer Example: Game of Life

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Game of Life For Each Line For Each Cell Solve Cell

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Game of Life For Each Line For Each Cell Solve Cell Generation LineCell Matrix

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Modularity Generation Module Matrix Module Line Module Cell Module

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Algorithm for the Generation Module 1. CurrentGen = 0 2. Solve for current Matrix 3. CurrentGen++ 4. If CurrentGen < MAX_GEN goto 2

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Solve Matrix 0. j = 1 1. Calculate line (j) 2. If j < MAX_LINE 2.1 j++ 2.2 goto 1. 3. STOP

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Calculate Line j 0. i = 0, tmp = 0 1. Calculate Cell i. 2. If alive, set location i in tmp to alive 3. If i < MAX_CELL 3.1 i++ 3.2 goto 1. 4. Store tmp in : even generation: i+16 odd generation : i-16

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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 alive 4. Return dead

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Count_Neighbors (index i,line j, center) 0. N = 0 1. If alive in location [i-1,j]: N=N+1 2. If not center: 2.1 If alive in location [i,j]: N=N+1 3. If alive in location [i+1,j]: N=N+1 4. Return N

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Algorithm implementation Algorithm How to do?What to do? The operation itselfcontrol

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The operations in the algorithm: Operations: Add Subtract

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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

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The operation: Module Calculate Line, instruction 2 If alive If dead Calculate_Line(j) = 0000000 OR tmp = 00000000 Result = 000000000 Calculate_Line(j) = 0001000 OR tmp = 00000000 Result = 000100000 The j-th location If alive, set location i in tmp to alive The Operation itself

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The operation: Module Calculate Line, instruction 2 If alive, set location i in tmp to alive tmp = OR(tmp,Calculate_Line(j)) The Operation itself

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The operations in the algorithm: Operations: Add Subtract OR The Operation itself

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Implementing instructions Module Count_Neighbors, instruction 1, 2.1, 3 decode(i-1) = 0001000 AND Line (j) = 00010100 Result = 00010000 decode(i-1) = 0001000 AND 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] The Operation itself

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Implementing instructions Module 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 Operation itself

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The operations in the algorithm: Operations: Add Subtract The logic AND + Check if zero The Operation itself

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Small ALU (arithmetic logic unit) Op selector MeaningResult 00AddRes = InputA+InputB 01SubractRes = InputA+ NOT(InputB)+1 10ANDRes = AND(InputA,InputB) 11DecodeRes = decode(InputA) The Operation itself

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Small ALU Status Bit The Operation itself

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Small ALU Status Bit The Operation itself ALU isZero Op InputB InputA

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Variables of the algorithm Count_Neighbors Line j – The current line i - The index we are processing N - The number of Neighbors so far tmp - temporary processing space

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Implementation of AND(line,decode(i+1)) Reg1 Reg2 Reg3 Regn

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Implementation of AND(line,decode(i+1)) Reg1 Reg2 Reg3 Regn ReadA ReadB 1 2 Connected like MUX 1

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Implementation of AND(line,decode(i+1)) Reg1 Reg2 Reg3 Regn ReadA ReadB 1 2 Decoder Enable Write Write Address Write Data

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Implementation of AND(line,decode(i+1)) Registers Data 1 Data 2 Data 1 Address Data 2 Address WriteAddress Write Data Write

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Variables of the algorithm Count_Neighbors VariableMeaningAddress CurrentLineHold the current line 0 IThe current index1 NThe Neighbor2 TmpTemporary space3 Constant 1 5 ControlVariableA flag to determine if the operation should be performed 6 CenterIs it the center7

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In generation 0 0 15 16 32 1 17 Current Generation Matrix, gen=0 Next generation Matrix I I+16

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In generation 1 0 15 16 32 1 17 Current Generation Matrix,gen=1 Next generation Matrix I+16 I

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Variables of the algorithm Count_Neighbors VariableMeaningAddress CurrentLineHold the current line 0 IThe current index1 NThe Neighbor2 TmpTemporary space3 Constant 1 5 ControlVariableA flag to determine if the operation should be performed 6 CenterIs it the center7

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Register/ALU circuit Registers Data 1 Address Data 2 Address WriteAddress Write ALU Op Extend 1 to 16 MUX R0R1 External Input 0 1 2

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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 The Operation itself

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Control Algorithm is zero[AND(line,decode(i-1))] Tmp = is zero[AND(line,decode(i-1))] Instruction The Operation itself t0. Tmp = i-1 t1. Tmp = decode(Tmp) t2. controlVariable = is zero[AND(CurrentLine, Tmp)] Micro-Instruction

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Micro instruction implementation t0. Data 1 Address = 1 Data 2 Address = 5 WriteAddress = 3 Write = 1 Op = 01 R0R1 = 01 Micro-Instruction The Operation itself a.Tmp = i+1 b.Tmp = decode(Tmp) c.controlVariable = is zero[AND(CurrentLine, Tmp)] Subtract i 1 tmp The result of the ALU

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Micro instruction implementation t1. Data 1 Address = 3 Data 2 Address = 0 WriteAddress = 4 Write = 1 Op = 11 R0R1 = 01 The Operation itself a.Tmp = i+1 b.Tmp = decode(Tmp) c.controlVariable = is zero[AND(CurrentLine, Tmp)] Decode tmp Irrelevant tmp The result of the ALU Micro-Instruction

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Micro instruction implementation t2. Data 1 Address = 0 Data 2 Address = 3 WriteAddress = 6 Write = 1 Op = 10 R0R1 = 00 The Operation itself a.Tmp = i+1 b.Tmp = decode(Tmp) c.controlVariable = is zero[AND(CurrentLine, Tmp)] And Line in register i tmp controlVariable The zero status bit Micro-Instruction

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Instruction Hierarchy Instruction Micro-Instruction Instruction Algorithmic Instruction The Operation itself

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Instruction Hierarchy Instruction t0: Micro-Instruction t n : Micro-Instruction t0: Micro-Instruction t n : Micro-Instruction Instruction Each micro instruction = 1 cycle Timing Variables

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Timing variables (example with 4 time variables) CP t0 t1 t2 t3 One instruction

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Generating Timing variables example with 16 timing variables CP Register 4bits Adder 1 Decoder t0 t15

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Control of Count_Neighbor

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0000 0001 0010 0011 0100 0101 0110 0111 1000

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Control of Count_Neighbor 0000 0001 0010 0011 0100 0101 0110 0111 1000

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Putting it all together: implementing what to do with ROM Current State TimingCVCD1D2WAWOpR0R1 t0t1t2t3 ROM Input ROM Output The current state (4 bits) The current timing variable (1 bits) Control variable (16bits) Center Register 7 (16bits)

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Putting it all together: implementing what to do with ROM Data 1 Address ROM Input ROM Output Data 2 Address Write-Data MUX control WriteAddress Write ALU Operation Current State TimingCVCD1D2WAWOpR0R1 t0t1t2t3

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Putting it all together: implementing what to do with ROM ROM Input ROM Output Current State Timing CVC D1D2WAWOpR0R1 t0t1t2t3 00011000 153101 00010100 30411101 00010010 03611000 00100001 000000001 t0. Tmp = i+1 t1. Tmp = decode(Tmp) t2. controlVariable = is zero[AND(CurrentLine, Tmp)] t3. do nothing

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Putting it all together: implementing what to do with ROM ROM Input ROM Output Current State Timing CVC D1D2WAWOpR0R1 t0t1t2t3 00011000 15310001 00010100 30411101 00010010 03611000 00100001 000000001 t0. Tmp = i+1 t1. Tmp = decode(Tmp) t2. controlVariable = is zero[AND(CurrentLine, Tmp)] t3. do nothing

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Putting it all together: implementing what to do with ROM ROM Input ROM Output Current State Timing CVC D1D2WAWOpR0R1 t0t1t2t3 00011000 15310001 00010100 30411101 00010010 03611000 00100001 000000001 t0. Tmp = i+1 t1. Tmp = decode(Tmp) t2. controlVariable = is zero[AND(CurrentLine, Tmp)] t3. do nothing

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Putting it all together: implementing what to do with ROM ROM Input ROM Output Current State Timing CVC D1D2WAWOpR0R1 t0t1t2t3 00011000 15310001 00010100 30411101 00010010 03611000 00100001 000000001 t0. Tmp = i+1 t1. Tmp = decode(Tmp) t2. controlVariable = is zero[AND(CurrentLine, Tmp)] t3. do nothing

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Control of Count_Neighbor 0000 0001 0010 0011 0100 0101 0110 0111 1000 t0. Set Current State 0001 t1. Set Current State 0001 t2. Set Current State 0001 t3. If ControlVariable=1 Set Current State 0010 t3. If ControlVariable=0 Set Current State 0011 Current State = 0001

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Putting it all together: implmenting control with ROM ROM InputROM Output Current State Timing CVC NextState t0t1t2t3 00011000 0100 0010 0001 1 0010 00010001 0 0011 Here is the branch.

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ROM Timing VariableCurrentState Registers ALU Extend 1 to 16 MUX R0R1 1 Result zerobit Op D1 D2 WA Write WriteData Next State Current State

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