Lecture 22: Logic Synthesis (1)

Transcription

1 Lecture 22: Logc Synthess (1) Sldes courtesy o Demng Chen Some sldes Courtesy o Pro. J. Cong o UCLA

2 Outlne Redng Synthess nd optmzton o dgtl crcuts, G. De Mchel, 1994, Secton Overvew Boolen lgebr Boolen unctons Boolen spce Boole s epnson Slde 2

3 Logc Synthess nd Optmzton Determne mcroscopc structure o the crcut Eplore (re-dely) trde-o Combntonl crcuts: * I/O dely Sequentl crcuts: * cycle-tme Enhnce crcut testblty Slde 3

4 Emple: Desgn Spce b c d Implement =pqrs wth: 2-nput or 3-nput AND gtes. Suppose re nd dely proportonl to number o nputs Slde 4

5 Emple: Desgn Evluton Spce re 7 6 () (c,d) 5 (b) dely Slde 5

6 Logc Synthess Problems Implementton styles: Two-level (e.g. PLA mcrocells). Mult-level (e.g. cell-bsed, rry-bsed). * Technology-ndependent optmzton * Technology mppng Opertons Combntonl. Sequentl: * Synchronous * Asynchronous Slde 6

7 Combntonl Logc Desgn Bckground Boolen lgebr Quntuple (B, +,, 0, 1) Bnry Boolen lgebr B={0, 1} Boolen uncton N-nput, sngle output: : B n B. N-nput, multple output: : B n B m. Incompletely speced: * don t cre symbol *. * : B n {0, 1, *} m. Slde 7

8 Some Propertes o Boolen Algebrc Systems + (b + c) = ( + b) + c (bc) = (b)c + = = + (b) = ( + b) = ( + b) = b (b) = + b ( ) = + b = + b Assoctvty Assoctvty Idempotence Idempotence Absorpton Absorpton De Morgn De Morgn Involuton Slde 8

9 Emple Smply = c + d + bd + bc Slde 9

10 The don t cre Condtons We don t cre bout the vlue o the uncton. Relted to the envronment: Input ptterns tht never occur (nput controllblty don t-cres). Input ptterns such tht some output s never observed (output observblty don t cres). Very mportnt or synthess nd optmzton Slde 10

11 Dentons Sclr uncton ON-set: subset o the domn such tht s true. OFF-set: subset o the domn such tht s lse. DC-set: subset o the domn such tht s don t cre. Multple-output uncton: Dened or ech component. Slde 11

12 Cubcl Representton bc bc b c b c bc bc b c b c c b Slde 12

13 Dentons (Cont d) Boolen vrbles. Boolen lterl: n nstnce o vrble or o ts complement. Product or cube: product o lterls. Implcnt: product mplyng vlue o uncton (usully TRUE). Hypercube n the Boolen spce. Mnterm: product o ll nput vrbles mplyng vlue o uncton (usully TRUE). Verte n the Boolen spce. Slde 13

14 Tbulr Representtons Truth tble: Lst o ll mnterms o uncton Implcnt tble or cover Lst o mplcnts o uncton sucent to dene uncton. Remrk: Implcnt tbles re smller n sze. Slde 14

15 Emple o Tbulr Representtons Emple o Truth Tble =b+ c; y=b+bc+c Emple o mplcnt tble =b+c; y=b+bc+c bc Xy bc Xy * * 11 Slde 15

16 Cubcl Representton o Mnterms nd Implcnts β β 101 c b α = bc+bc+bc+bc+bc 2 = bc+bc (smply) (smply) Slde 16

17 Coctor Functons Functon ( 1, 2,, n ). Coctor o wth respect to vrble : Coctor o wth respect to vrble : Boole s epnson theorem: 1, 2,...,1,..., n 1, 2,...,0,..., n,,..., 1,..., 2 n Slde 17

18 Emple Functon: = b + bc + c Coctors: = b + c = bc Epnson: = + = (b+c) + bc Slde 18

19 Unte Functons Functon ( 1, 2,, n ). Postve unte n when (set o mnterms o ncludes the set o mnterms o ) Negtve unte n when or or A uncton s postve / negtve unte when postve / negtve unte n ll ts vrbles. Slde 19

20 More on Boolen Functons Functon ( 1, 2,, n ). Boolen derence o w. r. to vrble : (whether s senstve to chnges n nput. When t s 0, the uncton does not depend on ) Consensus o w. r. to vrble : (the prt o on-set tht s ndependent o ) Smoothng o w. r. to vrble : (deletng ll ppernces o ) C S Slde 20

21 Emple o the Opertors on Boolen Functons: = b + bc +c bc c b c b () (b) b) The Boolen derence c) The consensus d) The smoothng (c) C S Slde 21 bc b c (d) b c bc

22 Summry Bsc Boolen representtons, propertes, nd optmztons Cubc representton A vsul wy to demonstrte Boolen opertons Co-ctor unctons Three types o opertons bsed on co-ctors Net lecture Logc Synthess (2) Slde 22