1. Chapter 3 Continued Logic Gates Logic Chips Combinational Logic Timing Sequential Logic Flip Flops Registers Memory State Machines

2. Logical Completeness Can implement ANY truth table with AND, OR, NOT. 1. AND combinations that yield a "1" in the truth table. 2. OR the results of the AND gates. ALSO: Can implement ANY truth table with ONLY NANDS. Can implement ANY truth table with ONLY NORS.

3. 1 Bit Full Adder

4. 4 Bit Full Adder 1 bit adder4 bit adder How many gate delays will it take before all of the outputs are correct?

5. Programmmable Logic Arrays (PLAs)

6. Programmable Logic Arrays (PLAs) Any combinational logic function can be realized as a sum of products. Idea: Build a large AND-OR array with lots of inputs and product terms, and programmable connections. –n inputs AND gates have 2n inputs -- true and complement of each variable. –m outputs, driven by large OR gates Each AND gate is programmably connected to each output’s OR gate. –p AND gates (p<<2 n ) –designation is n x m, p ANDs

7. Example: 4x3 PLA, 6 product terms --- X locates a fuse that can disconnect a line

8. Programmable Array Logic (PALs) How beneficial is product sharing? –Not enough to justify the extra fuse array PALs ==> fixed OR array –Each AND gate is permanently connected to a certain OR gate. Example: PAL16L8

9. 10 primary inputs 8 outputs, with 7 ANDs per output 1 AND for 3-state enable 6 outputs available as inputs –more inputs, at expense of outputs –two-pass logic, helper terms Note inversion on outputs –output is complement of sum- of-products –newer PALs have selectable inversion

10. Designing with PLAs Compare number of inputs and outputs of the problem with available resources in the PAL Write equations for each output using programming language like ABEL (Xilinx) Note: VHDL and Verilog are popular computer hardware design languages. ABEL is primarily used for specifying Programmed Logic.

11. Basic SR Flip Flop Nor Gates: Nand Gates: a 1 on S or R sets/resets the FF a 0 on S or R sets/resets the FF S R | Q n+1 0 0 | Q n 0 1 | 0 1 0 | 1 1 1 | Indeterminate S R | Qn+1 0 0 | Indeterminate 0 1 | 1 1 0 | 0 1 1 | Qn

12. Clocked SR Flip Flop S, R are nominally 0, a 1 on S or R will set/reset the FF AFTER the Clock Pulse S R | Qn+1 0 0 | Qn 0 1 | 0 1 0 | 1 1 1 | Indeterminate

13. D Flip Flop (D Latch) D | Qn+1 0 | 0 1 | 1

14. Positive Edge Triggered Flip Flop (7474)

15. Master Slave Flip Flop Master sets on rising edge of CP, Slave sets on falling edge of CP. (or visa versa depending on the particular Master Slave)

16. Toggle Flip Flop Toggles on CP when T =1 T | Qn+1 0 | Q n 1 | not Q n

17. JK Flip Flop J K | Qn+1 0 0 | Q n 0 1 | 0 1 0 | 1 1 1 | not Q n

18. JK as a Universal Flip Flop JK as an SR – use set and pre inputs JK as a Toggle – connect J and K JK as a D – connect NOT J to K