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9.2 STATIC HAZARDS IN TWO-LEVEL COMBINATIONAL LOGIC CIRCUITS 397

Procedure for Detection and Elimination of Static Hazards in Combinational Logic
Circuits

1. Identify the couple terms in an SOP or POS expression.
2. OR their consensus (RPI) P-terms to the SOP expression, or AND their consensus
s-terms to the POS expression.
3. Reject any set of two terms containing more than one couple variable. Remember:
Only one variable is allowed to change in a static hazard transition. All other variables
must be constant.
4. Read the initial and final states from the coupled terms in a hazardous transition by
using minterm code for SOP and maxterm code for POS.

As an example, consider the following minimum SOP function of four variables showing
two hazard transitions together with the corresponding hazard cover for each:

0001 0011
~^ ABC. (9.5)
Hazard cover
0100 0101

In this expression, NAND/INV logic is assumed with inputs that arrive active high. Here,
the hazard cover ABC is the ANDed residues (consensus p-term) of coupled terms BCD and
A CD, where D is the coupled variable. And hazard cover ABD is the ANDed residues of
couple terms A CD andfiC, where C is the coupled variable. These static 1-hazard transitions
are illustrated in the K-map of Fig. 9.6a by using arrows indicating a 1 —> 0 change in the
couple variable. The consensus terms can be seen to cover the hazard transitions (arrows).

CD C
AB\ 00 01 ' 11 10
00

01

11
A
10
8 9 I lo /
^^ SOP
D
(a)
FIGURE 9.6
K-map representation of static hazards in the function F represented by Eq. (9.5) and by Eq. (9.6).
(a) Static 1 hazard transitions, (b) Static 0 hazard transitions.