Describing Combinational circuits in BSV

Transcription

1 Decriing Comintionl circuit in BSV Arvind Computer Science & Artificil Intelligence L. Mchuett Intitute of Technology Ferury 13, L03-1

2 Three imple comintionl circuit NOT 0 1 = ~ 1 0 AND = OR = + Any comintionl circuit cn e uilt uing thee three gte Ferury 13, L03-2

3 Some other fmou gte NAND = ~( ) NOR = ~(+) Cn you expre thee gte uing NOT, AND, nd OR gte? Ferury 13, L03-3

4 Excluive OR (XOR): nother fmou gte XOR = From the Truth Tle XOR produce 1 when either (=0) AND (=1) or (=1) AND (=0). Hence, = ~ + ~ Cn you expre XOR uing NOT, AND, nd OR gte? Ferury 13, L03-4

5 Pictoril convention for drwing inverter All thee repreent the me circuit Ferury 13, L03-5

6 Nomenclture We ue the word in ech of the following ctegorie interchngely comintionl circuit, Boolen expreion, Boolen circuit gte, Boolen opertor We ue vrile to nme wire in comintionl circuit Ferury 13, L03-6

7 Decriing Complex Comintionl circuit A comintionl circuit with n input vrile nd m output h 2 n row nd m column in it Truth Tle repreenttion Truth Tle re not prcticl repreenttion for circuit with lrge numer of input Circuit digrm re even more tediou to drw Both repreenttion re uele when we wnt computer to imulte the ehvior of circuit, i.e., determine the output given n input We will ue progrmming lnguge clled Bluepec Sytem Verilog (BSV) to expre ll circuit Ferury 13, L03-7

8 Hlf Adder A B S C function h(, ); = ^ ; c = & ; return {c,}; XOR AND Boolen eqution = c = endfunction Not quite correct need type nnottion Ferury 13, L03-8

9 Hlf Adder corrected function Bit#(2) h(bit#(1), Bit#(1) ); Bit#(1) = ^ ; Bit#(1) c = & ; return {c,}; endfunction Bit#(1) type declrtion y tht i one it wide {c,} repreent it conctention How ig i {c,}? 2 it Ferury 13, L03-9

10 BSV note function Bit#(2) h(bit#(1), Bit#(1) ); Bit#(1) = ^ ; Bit#(1) c = & ; return {c,}; endfunction h cn e ued lck-ox long we undertnd it type ignture Suppoe we write t = h(,) then t i two it quntity repreenting c nd vlue We cn recover c nd vlue from t y writing t[1] nd t[0], repectively h c Ferury 13, L03-10

11 Full Adder 1-it dder with crry-in input c_in f h h c_out function Bit#(2) f(bit#(1), Bit#(1), Bit#(1) c_in); Bit#(2) = h(, ); Extrct the um it Bit#(2) c = h([0], c_in); Extrct the crry it Bit#(1) c_out = [1] c[1]; return {c_out, c[0]}; endfunction h i eing ued lck-ox; f code i imply wiring digrm Ferury 13, L03-11

12 The let yntx c_in f h h c_out function Bit#(2) f(bit#(1), Bit#(1), Bit#(1) c_in); let = h(, ); let c = h([0], c_in); let c_out return {c_out, c[0]}; endfunction = [1] c[1]; No need to write the type if the compiler cn deduce it Ferury 13, L03-12

13 Type A type i grouping of vlue: Integer: 1, 2, 3, Bool: True, Fle Bit: 0,1 More complex type cn e defined in term of impler type Tuple2#(Integer, Integer) repreent pir of Integer function Integer fnme (Integer rg) repreent function from Integer to Integer nd i nmed fnme Every expreion in BSV progrm h type; ometime it i pecified explicitly nd ometime it i deduced y the compiler Thu, we y n expreion h type or elong to type An expreion h exctly one type Ferury 13, L03-13

14 Prmeterized type: # A type declrtion itelf cn e prmeterized y other type Prmeter re indicted y uing the yntx # For exmple Bit#(n) repreent n it nd cn e intntited y pecifying vlue of n Bit#(1), Bit#(32), Bit#(8), Ferury 13, L03-14

15 Type ynonym typedef Bit#(8) Byte; typedef Bit#(32) Word; typedef Bit#(32) Dt; typedef Tuple2#(,) Pir#(type ); typedef Int#(n) MyInt#(numeric type n); Ferury 13, L03-15

16 Type declrtion veru deduction The progrmmer write down type of ome expreion in progrm nd the compiler infer the type of the ret of expreion If the type inference cnnot e performed or the type declrtion re inconitent then the compiler complin function Bit#(2) f(bit#(1), Bit#(1), Bit#(1) c_in); Bit#(2) = h(, ); Bit#(2) c = h([0], c_in); type error? Bit#(2) c_out = [1] c[1]; return {c_out, c[0]}; endfunction Type checking prevent lot of illy mitke Ferury 13, L03-16

17 Selector nd Multiplexer Ferury 13, L03-17

18 Selecting wire: x[i] Contnt Selector: e.g., x[2] x0 x1 x2 x3 [2] Dynmic elector: x[i] x0 x1 x2 x3 ume x i 4 it wide no hrdwre; x[2] i jut the nme of wire x0 x1 x2 x3 i [i] x0 x1 x2 x i 4-wy mux Ferury 13, L03-18

19 A 2-wy multiplexer 0 BSV Python 1 A mux i imple conditionl expreion (==0)? : ; if == 0 ele Gte-level implementtion If nd re n-it wide then thi tructure will e replicted n time Ferury 13, L03-19

20 A 4-wy multiplexer ce ({1,0}) mtche 0: ; 1: ; 2: c; 3: d; endce def mux(,, ): if == 0: return elif == 1: return elif == 2: return c ele: return d c d n-wy mux cn e implemented uing n-1 two-wy muxe 0 1 Ferury 13, L03-20

21 Shift opertor Ferury 13, L03-21

22 Logicl right hift y 2 c d Rotte Fixed ize hift opertion i chep in hrdwre jut wire the circuit ppropritely Other type of hift re imilr c d c d c d Arithmetic ueful for multipliction nd diviion y 2 n Ferury 13, L03-22

23 Logicl right hift y n Suppoe we wnt to uild hifter which hift vlue x y n where n i etween 0 nd 31 One wy to do thi i y connecting 31 different hifter vi mux x hr0 hri hr31 How mny 2-wy one-it muxe re needed to implement thi tructure? n*(n-1) n 0 31 Cn we do etter? Ferury 13, L03-23

24 Logicl right hift y n Shift n cn e roken down into log n tep of fixed-length hift of ize 1, 2, 4, For exmple, we cn perform Shift 3 (=2+1) y doing hift of ize 2 nd 1 Shift 5 (=4+1) y doing hift of ize 4 nd 1 Shift 21 (=16+4+1) y doing hift of ize 16, 4 nd 1 For 32-it numer, 5-it n cn pecify ll the needed hift 3 10 = , 5 10 = , = The it encoding of n tell u which hifter re needed; if the vlue of the i th (let ignificnt) it i 1 then we need to hift y 2 i it Ferury 13, L03-24

25 Conditionl opertion: hift veru no-hift We need mux to elect the pproprite wire: if i one the mux will elect the wire on the left otherwie it would elect wire on the right (==0)?{,,c,d}:{0,0,,}; Ferury 13, L03-25

26 Logicl right hift circuit Define log n hifter of ize 1, 2, 4, Define log n muxe to perform prticulr ize hift Shift circuit cn e expreed log n neted conditionl expreion where 0, 1.. Repreent the it of n We will explore uch deign in the next recittion Ferury 13, L03-26