1. June 20101 clock data Q-flop Flop dataQ clock Flip-flop is edge triggered. It transfers input data to Q on clock rising edge. Memory Elements

2. June 20102 Flop clk Flop clk Combinational Logic TCTC Static Sequencing by Flip-Flops One flip-flop is used on each cycle boundary. Tokens advance from one cycle to the next on rising edge.

3. June 20103 Sequencing Elements Timing Notations

4. June 20104

5. 5 Combinational Logic AY Flop clk DQ A Y D Q

6. June 20106 Max-Delay Constraints Q1 D2 TCTC clk FF1 clk FF2 clk Combinational Logic Q1 D2

7. Min-Delay Constraints Logic circuits cannot be too fast. Such malfunction is called race condition, hold time failure or min-delay failure. Otherwise the input data to next sequential circuit will change while it is still holding its current data.

8. June 20108 Combinational Logic FF1 clk Q1 FF2 clk D2 Q1 D2 clk

9. July 20109 Clock Skew Clock should theoretically arrive simultaneously to all sequential circuits. Practically it arrives in different times. The differences are called clock skews. Clock skew consists of the following components: –Systematic is the portion existing under nominal conditions. It can be minimized by appropriate design. –Random is caused by process variations like devices’ channel length, oxide thickness, threshold voltage, wire thickness, width and space. It can be measured on silicon and adjusted by delay components.

10. June 201010 FF1 clk FF2 clk Combinational Logic Q1 D2 Q1 D2 clk TCTC