Learning Outcome

an ability to analyze and design combinational logic circuits

Learning Objectives

1. identify minterms (product terms) and maxterms (sum terms)
2. list the standard forms for expressing a logic function and give an example of each: sum-of-products (SoP), product-of-sums (PoS), ON set, OFF set
3. analyze the functional behavior of a logic circuit by constructing a truth table that lists the relationship between input variable combinations and the output variable
4. transform a logic circuit from one set of symbols to another through graphical application of DeMorgan’s Law
5. realize a combinational function directly using basic gates (NOT, AND, OR, NAND, NOR)
6. draw a Karnaugh Map (“K-map”) for a 2-, 3-, 4-, or 5-variable logic function
7. list the assumptions underlying function minimization
8. identify the prime implicants, essential prime implicants, and non-essential prime implicants of a function depicted on a K-map
9. use a K-map to minimize a logic function (including those that are incompletely specified) and express it in either minimal SoP or PoS form
10. use a K-map to convert a function from one standard form to another
11. calculate and compare the cost (based on the total number of gate inputs plus the number of gate outputs) of minimal SoP and PoS realizations of a given function
12. realize a function depicted on a K-map as a two-level NAND circuit, two-level NOR circuit, or as an opendrain NAND/wired-AND circuit
13. define and identify static-0, static-1, and dynamic hazards
14. describe how a static hazard can be eliminated by including consensus terms
15. describe a circuit that takes advantage of the existence of hazards and analyze its behavior
16. draw a timing chart that depicts the input-output relationship of a combinational circuit
17. identify properties of XOR/XNOR functions
18. simplify an otherwise non-minimizable function by expressing it in terms of XOR/XNOR operators
19. describe the genesis of programmable logic devices
20. list the differences between complex programmable logic devices (CPLDs) and field programmable gate arrays (FPGAs) and describe the basic organization of each
21. list the basic features and capabilities of a hardware description language (HDL)
22. list the structural components of an ABEL program
23. identify operators and keywords used to create ABEL programs
24. write equations using ABEL syntax
25. define functional behavior using the truth_table operator in ABEL
26. define the function of a decoder and describe how it can be use as a combinational logic building block
27. illustrate how a decoder can be used to realize an arbitrary Boolean function
28. define the function of an encoder and describe how it can be use as a combinational logic building block
29. discuss why the inputs of an encoder typically need to be prioritized
30. define the function of a multiplexer and describe how it can be use as a combinational logic building block
31. illustrate how a multiplexer can be used to realize an arbitrary Boolean function