1. Appendix A Logic Circuits

2. Logic circuits Operate on binary variables that assume one of two distinct values, usually called 0 and 1 Implement functions of logic variables Circuits have inputs and outputs Circuits are implemented using electronic logic gates

3. Standard logic gate symbols

4. Implementation of the XOR function using AND, OR, and NOT gates

5. Synthesis of logic functions Synthesis is the process of designing and implementing a logic circuit defined by its functional specification. The expression for f in the previous circuit is said to be in a sum-of-products form, because the OR and AND operations are sometimes called the sum and product functions.

6. Implementation of a logic function

8. Proving equivalence of expressions

9. Rules of binary logic

10. Minimization of logic expressions As illustrated in the previous example, a logic function can be implemented with circuits of different complexities. It is useful to minimize a logic expression to reduce the cost of the synthesized circuit.

11. Three-variable Karnaugh maps

12. Four-variable Karnaugh maps

13. Using don’t cares

14. NAND and NOR gates

15. Equivalence of NAND-NAND and AND-OR networks

16. Cascading of gates

17. Representation of logic values by voltage levels

18. Tri-state buffer

19. A basic latch implemented with NOR gates

20. Gated SR latch

21. Gated SR latch implemented with NAND gates

22. Gated D latch

23. Master-slave D flip-flop

24. A negative-edge-triggered D flip-flop

25. T flip-flop

26. JK flip-flop

27. Master-slave D flip-flop with Preset and Clear

28. Shift register

29. Parallel-access shift register

30. A 3-bit up-counter

31. A two-input to four-output decoder

32. A BCD-to-7-segment display decoder

33. A four-input multiplexer

34. Multiplexer implementation of a logic function

35. A block diagram for a PLD

36. Functional structure of a PLA

37. A simplified sketch of the previous PLA

38. An example of a PAL

39. Inclusion of a flip-flop in a PAL element

40. Organization of a CPLD

41. A conceptual block diagram of an FPGA

42. Sequential circuits A logic circuit whose output is determined entirely by its present inputs is called a combinational circuit (e.g. decoders and multiplexers). A logic circuit whose output depends on both the present inputs and the state of the circuit is called a sequential circuit (e.g. counters).

43. State diagram of a mod-4 up/down counter that detects the count of 2

44. State table

45. State assignment table

46. The next-state expressions are: The output expression is

47. Implementation of the up/down counter

48. Timing diagram for the designed counter

49. A formal model of a finite state machine