1. CS 140 Lecture 18 Professor CK Cheng 6/04/02

2. Part IV. System Designs Algorithm: { Input X, Y type bit-vector, start type boolean; Local-Object A, B type bit-vector; Output Z type bit-vector, done type boolean; Wait: If start’ goto Wait || done  1; S1: A  X || B  Y|| done  0; S2: If B >= 0 goto S4; S3: B  -B; S4: If A >= B goto S6; S5: A  A + 1 || B  B+1 || goto S4; S6: Z  4 * A || done  1 || goto Wait; }

3. Data Control C 1-7 (A > B)Sign (B) X Y start Z done Z = 4 [ X + |Y| / 2] if X< |Y| 4x otherwise

4. A  X B  Y B  -B A  A + 1 B  B – 1 Z  4A (A >= B) (B >= 0) operation A  Load (X) B  Load (Y) B  CS (B) A  INC (A) B  DEC (B) Z  Load (A) Z  SHL (Z) Comp (A, B) Sign (B) control C 1 C 2 C 3 C 4 C 5 C 6 C 7

5. B A C2C2 C3C3 C5C5 C1C1 C4C4 X INC Comp Z Control Unit B C6C6 C7C7 CS DEC Y C1C1 C2C2 C3C3 C4C4 C5C5 C6C6 C7C7 start done

6. S0: S1: S2: S3: S4: S5: S6: S7: S8: If start’, goto S0, else goto S1 A  X || B  Y || done  0 || goto S2 If B goto S4, else goto S3 B  CS (B), goto S4 If k goto S6, else goto S5 A  INC (A), B  DEC (B), goto S4 Z  A goto S7 Z  SHL (z), goto S8 Z  SHL (z), done 1, goto S0

7. State Machine S0 S1 S2 S3 S4 S8 S7 S6 S5 k’ k B B’ start’ start