Systems I. Logic Design I. Topics Digital logic Logic gates Simple combinational logic circuits

Transcription

1 Systems I Logic Design I Topics Digitl logic Logic gtes Simple comintionl logic circuits

2 Simple C sttement.. C = + ; Wht pieces of hrdwre do you think you might need? Storge - for vlues,, C Computtion logic - to compute + wy to tell the computer to retrieve the vlues from storge, dd them together, nd put the result ck in storge This could e ccomplished with single commnd (instruction) or with multiple of them. 2

3 Overview of Logic Design Fundmentl Hrdwre Requirements Communiction How to get vlues from one plce to nother Computtion Storge its re Our Friends Everything expressed in terms of vlues nd Communiction Low or high voltge on wire Computtion Compute oolen functions Storge Store its of informtion 3

4 Digitl Signls Voltge Time Use voltge thresholds to extrct discrete vlues from continuous signl Simplest version: -it signl Either high rnge () or low rnge () With gurd rnge etween them Not strongly ffected y noise or low qulity circuit elements Cn mke circuits simple, smll, nd fst 4

5 Computing with Logic Gtes nd Or Not Logic gtes constructed from trnsistors Outputs re oolen functions of inputs Respond continuously to chnges in inputs With some, smll dely = && = =! Rising Dely Flling Dely && Voltge Time 5

6 Truth Tles nd Or Not = && = =! 6

7 7 c Wht this? c =!(( && ) c) = ~(* + c) c c

8 Comintionl Circuits cyclic Network Primry Inputs Primry Outputs cyclic Network of Logic Gtes Continously responds to chnges on primry inputs Primry puts ecome (fter some dely) oolen functions of primry inputs 8

9 it Equlity it equl HCL Expression eq ool eq = (&&) (!&&!) Generte if nd re equl Hrdwre Control Lnguge (HCL) Very simple hrdwre description lnguge oolen opertions hve syntx similr to C logicl opertions Weʼll use it to descrie control logic for processors 9

10 Hrdwre Control Lnguge Very simple hrdwre description lnguge Cn only express limited spects of hrdwre opertion Prts we wnt to explore nd modify Dt Types ool: oolen,, c, int: words,, C, Sttements Does not specify word size---ytes, 32-it words, ool = ool-expr ; int = int-expr ;

11 HCL Opertions Clssify y type of vlue returned oolen Expressions Logic Opertions &&,,! Word Comprisons ==,!=, <, <=, >=, > Set Memership in {, C, D }» Sme s == == C == D Word Expressions Word Expressions Cse expressions [ : ; : ; c : C ] Evlute test expressions,, c, in sequence Return word expression,, C, for first successful test

12 Word Equlity Word-Level Representtion it equl it equl eq 3 eq 3 = Eq HCL Representtion Eq ool Eq = ( == ) it equl it equl eq eq 32-it word size HCL representtion Equlity opertion Genertes oolen vlue 2

13 it-level Multiplexor s it MUX HCL Expression ool = (s&&) (!s&&) Control signl s Dt signls nd Output when s=, when s= 3

14 Word Multiplexor s Word-Level Representtion s 3 3 MUX Out HCL Representtion int Out = [ s : ; : ; ]; Select input word or depending on control signl s HCL representtion Cse expression Series of test : vlue pirs Output vlue for first successful test 4

15 HCL Word-Level Exmples Minimum of 3 Words C MIN3 Min3 4-Wy Multiplexor int Min3 = [ < && < C : ; < && < C : ; : C; ]; Find minimum of three input words HCL cse expression Finl cse gurntees mtch How would you uild this? s s D D D2 D3 MUX4 Out4 int Out4 = [!s&&!s: D;!s : D;!s : D2; : D3; ]; Select one of 4 inputs sed on two control its HCL cse expression Simplify tests y ssuming sequentil mtching 5

16 Simple computtions re just comintionl logic circuits One it dder Sum = * + *C in + *C in C + C in C = ^^Cin = **C in + **C in + **C in + **C in Sum How do you do sutrct? Four it dder How do you do multiply? Sum Sum 3 Sum 2 Sum Sum 6

17 rithmetic Logic Unit 2 3 Y X L U OF ZF SF X + Y Y X L U OF ZF SF X - Y Y X L U OF ZF SF X & Y Y X L U OF ZF SF X ^ Y Comintionl logic Continuously responding to inputs Control signl selects function computed Corresponding to 4 rithmetic/logicl opertions in Y86 lso computes vlues for condition codes OF = overflow flg, ZF = Zero Flg, SF = Sign Flg 7

18 rithmetic Logic Unit <s,s> = <s,s> = <,s> = <s,s> = Y X L U OF ZF SF X + Y Y X L U OF ZF SF X - Y Y X L U OF ZF SF X & Y Y X L U OF ZF SF X ^ Y int Out = [!s&&!s: X+Y;!s&&s: Y-Y; s&&!s: X&Y; : X^Y; ]; 8

19 Summry Tody sic logic elements Comintionl logic circuits Truth tles, gtes ggregting logic elements Multiplexors, LUs, etc. Next Time Circuits tht rememer 9