1. CS 140 Lecture 19 Professor CK Cheng 12/05/02

2. Sequential Machine Standard Modules Combinational Sequential System Designs

3. Algorithm: { Input X, Y start Local-Object A, B Output W, Z done S1: If start’ goto S1; S2: done  0 || A  X || B  Y || W  0 S3: A  Add(A,B) || W  INC(W) S4: If A’ goto S3 S5: Z  A || done  1 || goto S1 }

4. A B C1C1 C2C2 C3C3 Y Add X A INC W C4C4 C5C5 C1, A  X C2, A  Add(A,B) C3, B  Y C4, W  0 C5, W  INC(W)

5. Control A Start C 1 -- C 5 done

6. S1 S2 S3 S4 S5 A A’ start’ start S1: done = 1 S2: C1 = C3 = C4 = 1 S3: C2 = C5 = 1 S4: S5: done = 1 1000110001 0100001000 0010000100 0100001000 0100001000 0010000100 doneC1 C2 C3 C4 C5 S1 S2 S3 S4 S5

7. start start’ S5 S1 S2 S3 A A’ S4 C2 C5 C1 C3 C4 done

8. Adders Id a b c in carry sum 0 0 0 0 0 0 1 0 0 1 0 1 2 0 1 0 0 1 3 0 1 1 1 0 4 1 0 0 0 1 5 1 0 1 1 0 6 1 1 0 1 0 7 1 1 1 1 1 1.Full Adder Design a FA with 2:1 Muxes FA a b Sum c out c in

9. a01a01 00 01 10 11 0 0 0 1 0 1 1 1 l 0 (b,c) l 1 (b,c) b c C out l001l001 c = 0 0 c = 1 0 1 l 2 = 0 l 3 = c b l101l101 c = 0 0 1 c = 1 1 l 4 = c l 5 = 1 b 0 1 a b C out 0 1 c 1 l1l1 b 0 1 0 c l0l0 l2l2 l3l3 l4l4 l5l5

10. 0 1 a b Sum 0 1 b 0 1 c c’ c abCin ab’c’ a’bc’ a’b’c

11. Adders Serial adder w/ SR FF aiai bibi sisi id 0 1 2 3 4 5 6 7 a i 0 1 b i 0 1 0 1 c i 0 1 0 1 0 1 0 1 S 0 - 0 - 1 - R - 1 - 0 - 0 c i+1 0 1 0 1 Q(t) Q(t+1) Use excitation table to find SR aiai bibi sisi SRSR Q c in