Arithmetic Logic Unit (ALU) Storage Elements. Today s Lecture

Transcription

1 Arithmetic Logic Unit (ALU) Storge Elements Computer Science 4 Tody s Lecture Homework #4 coming soon Building the uilding locks Outline Review igitl uilding locks An Arithmetic Logic Unit (ALU) Storge Elements Register File Reding Chpter 4.2 strt reding 4. & 4.3 2

2 Review: Boolen Functions nd Expressions F(A, B, C) = (A * B) + (~A * C) A B C F 3 Review: Boolen Gtes Gtes re electronics devices tht implement simple Boolen functions Exmples AN(,) OR(,) NOT() XOR(,) NAN(,) NOR(,) XNOR(,) 4

3 Review: Boolen Functions, Gtes nd Circuits Circuits re mde from network of gtes. (function compositions). XOR(,) F = ~* + ~* XOR(,) F 5 Circuit Exmple: ecoder I I 2 3 6

4 Circuit Exmple: 2x MUX Multiplexor (MUX) selects one of mny inputs y MUX(A, B, S) = (A * S) + (B * ~S) s B Gte Gte 3 Y = (A * S) + (B * ~S) A Gte 2 S 7 Exmple 4x MUX 3 c d y c d 2 y 2 s s S 8

5 Arithmetic nd Logicl Opertions in ISA Wht opertions re there? Arithmetic Logic Unit (ALU) Hrdwre tht performs opertions Only one opertion t time How do we implement the opertions? Consider AN, OR, NOT, nd A Input is two its, output 9 Truth Tle for -it Addition + C in Sum C out Wht is the circuit for Sum nd for Cout?

6 A -it Full Adder Cin Sum + Cout C in Sum C out Exmple: 4-it dder S3 S2 S S C out Full Adder Full Adder Full Adder Full Adder C in This is clled Ripple Crry Adder: There re fster, more complex dder circuits. 2

7 ALU Slice (Almost) C in 3 2 F + NOT 2 OR 3 AN Adder 2 C ou t F 3 Sutrction How do we perform integer sutrction? Wht is the hrdwre (circuit)? 4

8 ALU Slice C in 3 2 A F NOT - 2 OR - 3 AN ~Add/Su Adder 2 C ou t F 5 Exmple: 2 (= 53 ) + 2 (= 42 ) 2 (=-33 ) Overflow Exmple2: 2 (=-43 ) + 2 (=-54 ) 2 (= 3 ) Exmple3: 2 (= 53 ) + 2 (=-22 ) 2 (= 3 ) Exmple4: 2 (= 2 ) + 2 (= 42 ) 2 (= 63 ) 6

9 Overflow etection for 4-it dder OVERFLOW S3 S2 S S C out Full Adder Full Adder Full Adder Full Adder C in The ALU Overflow = Zero n- n-2 ALU Slice ALU Slice ALU Slice ALU Slice ALU control n- n- n-2 n-2 8

10 Astrction: The ALU Generl structure Two opernd inputs Control inputs ALU Opertion Input A Zero ALU Result We cn uild circuits for Multipliction ivision They re more complex Input B Crry Out Overflow 9 The Shift Opertion Consider n 8-it mchine How do I implement the shift opertion? 2

11 Shifter 2 Summry thus fr Given Boolen function, generte circuit tht relizes the function. Constructed circuits tht cn dd nd sutrct. The ALU: circuit tht cn dd, sutrct, detect overflow, compre, nd do it-wise opertions (AN, OR, NOT) Shifter Next up: Storge Elements: Registers, Ltches, Buses 22

12 Memory Elements All the circuits we looked t so fr re comintionl circuits: the output is Boolen function of the inputs. We need circuits tht cn rememer vlues. (registers) The output of the circuit is function of the input AN function of stored vlue (stte). Circuits with memory re clled sequentil circuits. 23 Set-Reset Ltch R R S S R S - on t set oth S & R to 24

13 Set-Reset Ltch (Continued) R R S S Time S R 25 t Ltch ( Ltch) E nle t E - Time oes not ffect Output E 26

14 Flip-Flop C ltch E ltch E On C is trnsferred to the first ltch nd the second is stle. On C the output of the first stge is trnsferred to the second (output), nd the first stge is stle. Output chnges only on the edge of clock 27 Register File Register File = the set of loctions for register vlues E.g., it registers How do I uild Register File using Flip-Flops? Wht other components do I need? 28

15 Register File Circuit to determine which of 32 registers? Circuit to get just the dt from one of 32 registers? 29 Tri-Stte river The Tri-Stte driver is like (one directionl) switch: When the Enle is on (E=) it trnsfers the input to the output. When the Enle is off (E=) it disconnects the output. E E - Z E Z :- High Impednce 3

16 Bus Connections The Bus: Mny to mny connections. Mutul exclusion: At most one Enle is on! Control must ensure this! Note: Bus sometimes used to denote multiple prllel wires 3 Register Cells on us IE E ltch OE IE E ltch OE IE E ltch OE IE E ltch OE One cn source nd sink from ny cell on the us y ctivting the right controls, IE--input enle, nd OE--output enle. 32

17 t-in 3-Port Register Cell Bus-C Bus-B Complement Bus-A in E nle OutA OutB Stores one it of register Cn Red onto Bus-A & Bus-B nd Write from Bus-C Simultneously 33 3-Port Register File EC EA EB Bus-C Bus-B Bit- Bus-A Bus-C Bus-B Bit- Bus-A 34

18 Address ecode Circuit t-in Bus-C Bus-B Register ddress: E nle OutA Bus-A OutB A A EA B B EB C C EC 35 Register File (Four 4-it Registers) Reg-3 Reg-2 Reg- Reg- A3 B3 C3 A2 B2 C2 A B C A B C A-En Add-A Add-A B -En Add-B Add-B C -En Add-C Add-C 36

19 igitl Logic Summry Given Boolen function, generte circuit to relize the function. Constructed circuits tht cn dd nd sutrct. The ALU: circuit tht cn dd, sutrct, detect overflow, compre, nd do it-wise opertions (AN, OR, NOT) Shifter Memory Elements: SR-Ltch, Ltch, Flip-Flop Tri-stte drivers & Bus Communiction vs. MUX Register Files Control Signls modify wht circuit does with inputs ALU, Shift, Register Red/Write 37 The ALU & Shifter Summry Storge elements S-R ltch, -Ltch, Flip-Flop Register File Next time Finite stte mchines HCL 38