CS220 Programming Principles

1. CS220Programming Principles 프로그래밍의 이해 2002 가을학기 Class 12: Logic Circuit Simulation 한 태숙

2. Event-driven Simulation • Example: Digital Circuit • function box : logic gates • wire : connections • delay: characteristics • Model • wire : computational objects which “hold” the signals -> make-wire • function boxes : procedure that enforce the correct relationships among signals

3. Half Adder (define a (make-wire)) (define b (make-wire)) (define d (make-wire)) (or-gate a b d) D A S E C B

4. Half-Adder (define (half-adder a b s c) (let ((d (make-wire)) (e (make-wire))) (or-gate a b d) (and-gate a b c) (inverter c e) (and-gate d e s) 'ok))

5. Full Adder (define (full-adder a b c-in sum c-out) (let ((s (make-wire)) (c1 (make-wire)) (c2 (make-wire))) (half-adder b c-in s c1) (half-adder a s sum c2) (or-gate c1 c2 c-out) ’ok))

6. Wire + Delay • Constructor : (make-wire) • (get-signal <wire>) • returns the current value of the signal on the wire • (set-signal! <wire> <new-value>) • changes the value of the signal on the wire • (add-action! <wire> <procedure of no args>) • asserts that the designated procedure should be run whenever the signal on the wire changes value • after-delay : simulates propagation delay

7. Gate Not (define (inverter input output) (define (invert-input) (let ((new-value (logical-not (get-signal input)))) (after-delay inverter-delay (lambda () (set-signal! output new-value))))) (add-action! input invert-input) 'ok) (define (logical-not s) (cond ((= s 0) 1) ((= s 1) 0) (else (error "Invalid signal" s))))

8. Gate AND (define (and-gate a1 a2 output) (define (and-action-procedure) (let ((new-value (logical-and (get-signal a1)(get-signal a2)))) (after-delay and-gate-delay (lambda () (set-signal! output new-value))))) (add-action! a1 and-action-procedure) (add-action! a2 and-action-procedure) 'ok)

9. Gate OR : exercise 3.28 (define (or-gate o1 o2 output) (define (or-action-procedure) (let ((new-value (logical-or (get-signal o1) (get-signal o2)))) (after-delay or-gate-delay (lambda () (set-signal! output new-value))))) (add-action! o1 or-action-procedure) (add-action! o2 or-action-procedure) 'ok)

10. Logical And, Logical Or (define (logical-and s1 s2) (cond ((and (= s1 1)(= s2 1)) 1) ((and (= s1 0)(= s2 1)) 0) ((and (= s1 1)(= s2 0)) 0) ((and (= s1 0)(= s2 0)) 0) (else (error "Invalid signal" s)))) (define (logical-or s1 s2) (cond ((and (= s1 1)(= s2 1)) 1) ((and (= s1 0)(= s2 1)) 1) ((and (= s1 1)(= s2 0)) 1) ((and (= s1 0)(= s2 0)) 0) (else (error "Invalid signal" s))))

11. Representing Wires (define (make-wire) (let ((signal-value 0) (action-procedures '())) (define (set-my-signal! new-value) (if (not (= signal-value new-value)) (begin (set! signal-value new-value) (call-each action-procedures)) 'done)) (define (accept-action-procedure! proc) (set! action-procedures (cons proc action-procedures)) (proc))

12. (define (dispatch m) (cond ((eq? m 'get-signal) signal-value) ((eq? m 'set-signal!) set-my-signal!) ((eq? m 'add-action!) accept-action-procedure!) (else (error "Unknown operation --WIRE" m)))) dispatch)) (define (call-each procedures) (if (null? procedures) 'done (begin ((car procedures)) (call-each (cdr procedures)))))

13. (define (get-signal wire) (wire 'get-signal)) (define (set-signal! wire new-value) ((wire 'set-signal!) new-value)) (define (add-action! wire action-procedure) ((wire 'add-action!) action-procedure))

14. The Agenda • (make-agenda) • constructor: returns a new empty agenda • (empty-agenda? <agenda>) • is true if the specified agenda is empty • (first-agenda-item <agenda>) • returns the first item on the agenda • (remove-first-agenda-item! <agenda>) • modifies the agenda by removing the first item • (add-to-agenda! <time> <action> <agenda>) • modifies the agenda by adding the given action procedure to be run at the specified time

15. Implementing Delay: After-delay • (current-time <agenda>) • return the current simulation time • We will define the-agenda as agenda data structure (define (after-delay delay action) (add-to-agenda! (+ delay (current-time the-agenda)) action the-agenda))

16. Driver Program - Propagate (define (propagate) (if (empty-agenda? the-agenda) ’done (let ((first-item (first-agenda-item the-agenda))) (first-item) (remove-first-agenda-item! the-agenda) (propagate))))

17. Probe - Detecting Signal (define (probe name wire) (add-action! wire (lambda () (newline) (display name) (display ” ”) (display (current-time the-agenda)) (display ” New-value= ”) (display (get-signal wire)))))

18. Setting Up Environment (define the-agenda (make-agenda)) (define inverter-delay 2) (define and-gate-delay 3) (define or-gate-delay 5) ; circuit description (define input-1 (make-wire)) (define input-2 (make-wire)) (define sum (make-wire)) (define carry (make-wire)) (probe 'sum sum) (probe 'carry carry) (half-adder input-1 input-2 sum carry)

19. Running the simulation > (set-signal! input-1 1) 'done > (propagate) sum 8 New-value = 1 'done > (set-signal! input-2 1) 'done > (propagate) carry 11 New-value = 1 sum 16 New-value = 0 'done

20. Implementing Agenda(I) (define (make-time-segment time queue) (cons time queue)) (define (segment-time s) (car s)) (define (segment-queue s) (cdr s)) (define (make-agenda) (list 0)) (define (current-time agenda) (car agenda)) (define (set-current-time! agenda time) (set-car! agenda time)) (define (segments agenda) (cdr agenda)) (define (set-segments! agenda segments) (set-cdr! agenda segments)) (define (first-segment agenda) (car (segments agenda))) (define (rest-segments agenda) (cdr (segments agenda)))

21. Implementing Agenda(II) (define (empty-agenda? agenda) (null? (segments agenda))) (define (remove-first-agenda-item! agenda) (let ((q (segment-queue (first-segment agenda)))) (delete-queue! q) (if (empty-queue? q) (set-segments! agenda (rest-segments agenda))))) (define (first-agenda-item agenda) (if (empty-agenda? agenda) (error "Agenda is empty -- FIRST-AGENDA-ITEM") (let ((first-seg (first-segment agenda))) (set-current-time! agenda (segment-time first-seg)) (front-queue (segment-queue first-seg)))))

22. Implementing Agenda(III) (define (add-to-agenda! time action agenda) (define (belongs-before? segments) (or (null? segments) (< time (segment-time (car segments))))) (define (make-new-time-segment time action) (let ((q (make-queue))) (insert-queue! q action) (make-time-segment time q)))

23. (define (add-to-segments! segments) (if (= (segment-time (car segments)) time) (insert-queue! (segment-queue (car segments)) action) (let ((rest (cdr segments))) (if (belongs-before? rest) (set-cdr! segments (cons (make-new-time-segment time action) (cdr segments))) (add-to-segments! rest)))))

24. (let ((segments (segments agenda))) (if (belongs-before? segments) (set-segments! agenda (cons (make-new-time-segment time action) segments)) (add-to-segments! segments))))