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392 CHAPTER 9 / PROPAGATION DELAY AND TIMING DEFECTS

Dynamic hazards: Multiple glitches that occur in the outputs from multilevel
circuits because of a change in an input for which there are three or more
asymmetric paths (delay-wise) of that input to the output.

Dynamic 0-»1 -»0-»1 Dynamic 1 -»0-»1 ->0
Hazard Hazard

Function hazards: A type of logic noise that is produced when two or more
inputs to a gate are caused to change in close proximity to each other.

In this chapter the discussion will center on how these hazards occur and how they can be
avoided or eliminated. Since the subject of hazards is also of considerable importance to
sequential machine design, it with be revisited in subsequent chapters.

9.2 STATIC HAZARDS IN TWO-LEVEL COMBINATIONAL LOGIC CIRCUITS

A single glitch that is produced as a result of an asymmetric path delay through an inverter
(or gate) is called a static hazard. The term "static" is used to indicate that the hazard
appears in an otherwise steady-state output signal. Thus, a static hazard is not "stationary"
or "motionless," as implied by the usual usage of the word static, but is quite unstationary
and transient.
The best way to introduce static hazard detection and elimination in combinational logic
is by means of simple examples. However, before proceeding further it will be helpful to
define certain terms that are used in identifying static hazards in SOP or POS combinational
logic circuits, and to provide a simple procedure for their elimination:

Coupled variable: An input variable that is complemented in one term of an
output expression and uncomplemented in another term.
Coupled term: One of two terms containing only one coupled variable.
Residue: That part of a coupled term that remains after removing the coupled
variable.
Hazard cover (or consensus term): The RPI required to eliminate the static
hazard:
AND the residues of coupled p-term to obtain the SOP hazard cover, or
OR the residues of coupled s-terms to obtain the POS hazard cover.

Note that in either case the RPI (redundant prime implicant) is a result of the application of
a consensus law given by Eqs. (3.14).

Static Hazard Detection and Elimination Static hazard detection involves identifying
the coupled terms in an logic expression. Static hazard elimination occurs when the con-
sensus p-term RPI is ORed to the SOP expression containing the static hazard, or when the
consensus s-term RPI is ANDed to the POS expression containing the static hazard. Note
that if the RPI is contained in a more minimum term, that term should be used.