1. Homework Your task is to design a regular structure such as Kronecker Lattice or Shannon Lattice using modern Quantum Dot Cellular Automata technology. Next slides show several example of such circuits. Please observe and understand in practical use the wire, the wire of inverters, the intersection, the fan- out, the way of creating inverters. These slides are shown to make you sensitive to several problems that may occur in practical circuit designs.

2. Majority Gate and its uses to realize AND and OR gates. Smaller inverters will be also shown

3. Majority Gate A B C M(A,B,C) M A B C A B 0 AND(A,B) A 1 C OR(A,C) Look also to lecture notes for explanation how this gate works

4. Coplanar wire-crossing Normal array goes horizontally Inverter chain goes vertically

5. Inverter

6. Realization of a circuit

9. This slide shows how you can use PowerPoint to create well-aligned to grid figures of wires and intersection of wires.

10. Homework Continued Your task is to design a regular structure such as Kronecker Lattice or Shannon Lattice using modern Quantum Dot Cellular Automata technology. Next slide show an example of such circuit. Please observe and understand in practical use the wire, the wire of inverters, the intersection, the fan-out, the way of creating inverters. Please observe the small shift between the left and right part of the schematics. Explain why it is done.

11. Shifted down by half cell. Explain why?

12. In this and next slides we give few examples of QD circuits to show how typical layout/logic problems are solved.

15. S1’ S0’

16. D Filp-Flop

18. Barrel Shifter

19. output 0 1 Input 1 Input 2 control Majority configured to AND Majority configured to OR This slide shows Shannon cell from a Lattice. Dimensions are wrong. Please explain how this works and improve the wiring sizes. Blue circles represent parts of wires that may be removed or not, depending on the function that is realized

20. The next slide shows the layout of connections to the cell in the 3*3 lattice. It has not all power of connecting from the recent paper. Think how to modify this circuit so that there will be possible to connections to left, two connections to top and two connections to right cells. (in a notation where circuit grows from bottom to top, here the circuit grows from left to right).

21. cell

22. 1 0 cntr exor This is Positive Davio Cell without connections to neighbors. The rules of neighborhood are not preserved. Correct this circuit and try to optimize it. Simplified and non-optimized Positive Davio Cell. Observe how EXOR is realized. Can you find a better way?

23. Next slide shows a general cell of reconfigurable FPGA with AND/EXOR cell. This cell can realize Positive and Negative Davio and Shannon (using exor). It allows for swapped expansions and for function A+ B+ XOR A+ B+ where A+ denotes arbitrary polarity of singal A. In the next slides inverters were not correctly realized. Think how this can be improved. There are two ways to realize inverters. Stand-alone and in wires.

24. 0 cntr 1 0 1

25. Final Homework Select on of the following and realize preserving all design rules. –A) Shannon Cell for 2*2 lattice –B) Positive Davio Cell for 2*2 lattice –C) General Cell for 2*2 lattice –D) General Cell for 3*3 lattice –E) General Cell for the paper with Mishchenko.