1. מבנה מחשב תרגול 2 מונים

2. Counters

3. תירגול 2 - מבנה מחשב3 Edge Triggering Important Issue:  The T Flip-Flop and the JK Flip-Flop 1-1 option are not stable since they are “toggle” operations.  From now all FFs are assumed down edge- triggered: Values are changed not when the clock is up, but at the exact moment the clock goes down – notice the circle notation  Edge Triggering mechanism can be seen in the lecture.

4. תירגול 2 - מבנה מחשב4 New Approach To Flip-Flops (1) Formerly, we presented each flip-flop’s Truth Table, i.e. the output as a function of former state (former output) and the inputs. 000 110 101 011 Former State InputOutput T Flip-Flop Example

5. תירגול 2 - מבנה מחשב5 New Approach To Flip-Flops (2) A new Approach: For each former output and desired output combination, what inputs do we need to transform from current to desired? This approach is more useful when creating counters.

6. תירגול 2 - מבנה מחשב6 New Approach To Flip-Flops (3)

7. תירגול 2 - מבנה מחשב7 Flip-Flop Concatenation T Flip-Flop has an interesting Attribute: 1 1 1010 1010 1010 (In red, is the clock down-edge)

8. תירגול 2 - מבנה מחשב8 Flip-Flop Concatenation (2) But doesn’t that resemble counting in binary? 000 100 010 110 001 101 011 111

9. תירגול 2 - מבנה מחשב9 Asynchronic Counter So we can use this attribute to create a simple n-digit binary counter.  (shown here with the equivalent 1-1 state JK Flip-Flop)

10. תירגול 2 - מבנה מחשב10 BCD Counter Can we count in a radix which is not ? Yes, we can even create a binary-coded decimal (BCD) Counter:

11. תירגול 2 - מבנה מחשב11 BCD Counter (2) To create it we used the diagram:

12. תירגול 2 - מבנה מחשב12 BCD Counter Concatenation If we can count to 10 (exclusive) we can count to 100, 1000 and so on…

13. תירגול 2 - מבנה מחשב13 BCD Counter Two problems:  Developing a custom-made, efficient, asynchronic counter, such as the BCD counter is difficult!  What if we want to create a non-consecutive counter easily?

14. תירגול 2 - מבנה מחשב14 Counting Sequence A cyclic sequence of binary numbers. For instance: 0,1,2,4,5,6,0,1,2,4,…

15. תירגול 2 - מבנה מחשב15 Synchronic Counter We want to implement a mechanism for counting in a given counting sequence. We’ll focus independently on each digit and the changes it undergoes.

16. תירגול 2 - מבנה מחשב16 Building A Sync. Counter Algorithm:  Choose a Flip-Flop type to use.  To each digit (column), allocate a Flip-flop.  For each digit (column) create a truth table in the following manner: For each state (line) do:  Mark state in current line as  Mark state in next line as  Determine the desired FF’s inputs by the tables. Those inputs are actually function results in the truth table. Simplify the truth table and implement the function

17. תירגול 2 - מבנה מחשב17 3-Bit Sync. Counter using T Flip-Flops (2)

18. תירגול 2 - מבנה מחשב18 3-Bit Sync. Counter using T Flip-Flops (1)

19. תירגול 2 - מבנה מחשב19 3-Bit Sync. Counter using T Flip-Flops (3)

20. תירגול 2 - מבנה מחשב20 3-Bit Sync. Counter using T Flip-Flops (3)

21. תירגול 2 - מבנה מחשב21 3-Bit Sync. Counter using T Flip-Flops (4)

22. תירגול 2 - מבנה מחשב22 Example using JK Flip-Flops (2)  Shown for the 0,1,2,4,5,6,0,1,2,4,5,6,… example We’ll do C as an example.

23. תירגול 2 - מבנה מחשב23 Example using JK Flip-Flops (1)

24. תירגול 2 - מבנה מחשב24 Example using JK Flip-Flops (3) JC: KC: 0XX1 0XX1 0 1 00011110 XX1X XX1X 0 1 00011110

25. תירגול 2 - מבנה מחשב25 Example using JK Flip-Flops (4)