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9.3 DETECTION AND ELIMINATION HAZARDS 403

A(H)
B(H) J
C(H) J
D(H)
n n

n n n n
(B+C+D)(H) i 1
(A+C+D)(H)

L H
EOS( )* o
* Indicates with hazard cover
FIGURE 9.9
Timing diagram for functions Lpos and LEGS without and with (*) hazard cover in accordance with
Eqs. (9.13) and (9.14).

hazards are static 0 hazards in L POs and L Eos rather than the static 1 hazards as in NSOP and
NXOP- Again notice that the static hazards in L EOS, like those in N XQR, are formed following
both a 0 —>• 1 and 1 —»• 0 change in the coupled variable. It is this characteristic that
distinguishes SOP and POS forms from XOP and EOS forms. The former types generate
static hazards on a single change of the coupled variable, whereas the latter types generate
static hazards on both 1 -> 0 and 0 —>• 1 changes in the coupled variable.

9.3.2 Methods for the Detection and Elimination of Static Hazards in Complex
Multilevel XOR-type Functions
Function minimization methods involving K-map XOR-type patterns and Reed-Muller
transformation forms are considered in detail in Chapter 5. For certain functions these
methods lead to gate-minimum forms that cannot be achieved by any other means. An
inspection of these forms reveals that they are of the general form

(9.15)

where a, ft, and F can be composed of SOP, POS, XOP, or EOS terms or some combination
of these. The XOP and EOS functions discussed in Subsection 9.3.1 are a special case of
Eq. (9.15), and the methods used there for the detection and elimination of static hazards
parallel those used for two-level logic discussed in Section 9.2. However, these simple
methods cannot be applied to the more complex functions considered in this subsection.
Now, use must be made of special graphic methods to assist in the determination of path
delay asymmetry according to Fig. 9.1.