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# CArcMOOC 03.03 - Sequential circuits

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Computer Architecture
Degree Program in Applied Computer Science
University of Urbino
http://informatica.uniurb.it/

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### CArcMOOC 03.03 - Sequential circuits

1. 1. Carc 03.03 alessandro.bogliolo@uniurb.it 03. Logic Networks 03.03. Sequential Circuits • Dealing with feedback • Finite state machines • Latches • Flip flops • Registers • Synchronous sequential circuits Computer Architecture alessandro.bogliolo@uniurb.it
2. 2. Carc 03.03 alessandro.bogliolo@uniurb.it Dealing with feedback s r y y' 0 0 ? ? 0 1 0 1 1 0 1 0 1 1 0 0 s r y y' y y' 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1
3. 3. Carc 03.03 alessandro.bogliolo@uniurb.it Sequential circuits: FSMs • Finite state machines (FSM): (S,I,O,f,g,s0) • Output function o=f(s,i) • Next-state function snext=g(s,i) • Representation: state diagram • Classification: • Combinational f:I  O • Sequential (Mealy’s) f:SxI  O g:SxI  S • Sequential (Moore’s) f:S  O g:SxI S • Asynchronous vs Synchronous
4. 4. Carc 03.03 alessandro.bogliolo@uniurb.it Moore’s FSM: example ON Light OFF Dark off on offon S = {ON,OFF} I = {on,off} O = {Light,Dark} f: S  O g: SxI  S state out in f g State Input Output Snext OFF off Dark OFF OFF on Dark ON ON off Light OFF ON on Light ON Case of a simple power supply system controlled by an on/off switch and monitored by a led
5. 5. Carc 03.03 alessandro.bogliolo@uniurb.it Mealy’s FSM: example ON OFF off, D on, D off, D test, D on, D test, L S = {ON,OFF} I = {on,off,test} O = {Light,Dark} f: SxI  O g: SxI  S state in,out f g State Input Output Snext OFF off Dark OFF OFF on Dark ON OFF test Dark OFF ON off Dark OFF ON on Dark ON ON test Light ON Case of a simple power supply system controlled by an on/off switch and monitored by a led when a test button is pressed
6. 6. Carc 03.03 alessandro.bogliolo@uniurb.it FSMs: example state input (sr) f g A 00 01 A A 01 01 A A 10 10 B A 11 00 A B 00 10 B B 01 01 A B 10 10 B B 11 00 B
7. 7. Carc 03.03 alessandro.bogliolo@uniurb.it Latch SR y y' y' s r f g 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 In order to use the circuit to store a bit, we need three input configurations to: •set y=1 regardless of the current state •set y=0 regardless of the current state •keep y unchanged SETRESET HOLD
8. 8. Carc 03.03 alessandro.bogliolo@uniurb.it Latch SR y y' y' s r f g 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 (s,r) = (1,0) SET (s,r) = (0,1) RESET (s,r) = (0,0) HOLD (s,r) = (1,1) NOT ALLOWED Notice that y’=NOTy for all allowed input configurations SETRESET HOLD
9. 9. Carc 03.03 alessandro.bogliolo@uniurb.it Flip Flop SR Clk S R s r 0 0 0 0 0 HOLD 0 0 1 0 0 HOLD 0 1 0 0 0 HOLD 0 1 1 0 0 HOLD 1 0 0 0 0 HOLD 1 0 1 0 1 RESET 1 1 0 1 0 SET 1 1 1 1 1 NOT ALLOWED
10. 10. Carc 03.03 alessandro.bogliolo@uniurb.it Flip Flop D Level Sensitive Clk D S R s r 0 0 0 1 0 0 HOLD 0 1 1 0 0 0 HOLD 1 0 0 1 0 1 RESET 1 1 1 0 1 0 SET
11. 11. Carc 03.03 alessandro.bogliolo@uniurb.it Flip Flop D Edge Triggered n
12. 12. Carc 03.03 alessandro.bogliolo@uniurb.it Registers ... n-bit register n 0 1 n-1
13. 13. Carc 03.03 alessandro.bogliolo@uniurb.it Synchronous Sequential Circuits General Mealy’s Moore’s f(s,i) g(s,i) f(s,i) g(s,i) f(s)g(s,i)