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PROBLEMS 415

PROBLEMS

9.1 A function Y is represented in the K-map of Fig. P9.1. Refer to the examples in Section
9.2 and do the following:
(a) Loop out a minimum SOP and POS cover and then use arrows in separate K-maps
to indicate the direction of the hazardous SOP and POS transitions that are present
in this function.
(b) Find the hazard covers and combine them with the minimum SOP and POS ex-
pressions. Also, show these covers on the appropriate K-maps.

ArXCD
AB\ oo 01 11 10
0 1 1 0
1 1 1 1

0 0 0 1
10 0 1 1 1

FIGURE P9.1

9.2 The following minimum SOP function contains both static 1-hazards and static 0-
hazards:

F = ABC + BD + ACD + BCD.

(a) Map and loop out this function in a fourth-order K-map and indicate the direction
of each SOP hazardous transitions on the map by using an arrow. Follow the
example in Fig. 9.6a.
(b) Find the hazard covers and add them to the original expression above.
(c) By following the example in Eq. (9.5), confirm that the same information can be
obtained directly from the minimum SOP expression just given.
(d) Repeat parts (a), (b), and (c) for the POS hazards (static 0-hazards) in the minimum
POS expression for this function.
(e) Use the gate/input tally (exclusive of possible inverters) to compare the SOP and
POS expressions with hazard cover included. Which result is simpler?
9.3 The following function contains a single static 1-hazard:

FSOP = ABC + AC + CD.

(a) From this expression (without using a K-map), determine the coupled terms, the
initial and final states of the hazardous transition, and the hazard cover to be added
to the expression. To do this, follow the example in Eq. (9.5).