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402 CHAPTER 9 / PROPAGATION DELAY AND TIMING DEFECTS

A(H)

B(H) 1 o

H
NSOP( ) J u u
u u u u
Bco(H) ;
ACD(H) 1

H
N p( r 1
XO
* Indicates with hazard cover
FIGURE 9.8
Timing diagram for functions N$QP and N\OP without and with (*) hazard cover in accordance with
Eqs. (9.11) and (9.12).

As an example, consider the reduced POS and EOS forms of function L, which are the
complements of function N in Eqs. (9.11) and (9.12), i.e., L = N. These POS and EOS
functions are represented by the following expressions, together with the hazard transitions
and hazard cover for each:

1011
__
= (A+B + C}(A + B + D)(A + B + C + D}(A + B + C + D)

0111 1111
'(B + C + D)(A + C + D) (9.13)
Hazard cover
1111 1011

LEOS = (A
{
0111 1111
.(B + C + DKA + C + D). (9.14)

Hazard cover
The coupled variables are A and B, and the coupled terms and hazard transitions are indi-
cated by arrows. The hazard cover terms for both the POS and EOS forms are (B + C + D)
and (A + C + D), each of which is the ORed residues of the respective coupled terms.
Notice that in both cases the hazard cover terms are ANDed to the original expressions.
The timing diagram in Fig. 9.9 illustrates the behavior of L POs and L EOs without and
with hazard cover. This behavior is similar to that of NSOP and NXOP in Fig. 9.8, but static