Detection of Static Hazards :

Detection of Static Hazards :

• Static hazards can be detected with the help of Boolean algebraic expressions in which a variable and its complement are treated as different i.e. as non related variables.
• This is because, under the transient conditions, a variable and its complement can momentarily have the some logic value.
• In order to detect static hazards, the Boolean expression of the network is first written in the form which is in the one to one correspondence with the network.
• This expression is then manipulated into a SOP form, for the detection of static-1 hazards. The expression is written in the POS form, for the detection of static-0 hazards.
• All the theorems except for the following, can be used for manipulation. A –A = 0, A + –A = 1, A + –AB = A + B
• This is because we have to treat A and –A as different variables, in transient analysis.
• However the laws such as A + AB = A and A (A + B) = A are to be employed.
• The resulting SOP or POS expressions after manipulation are called “transient normal formulas”.
• The product terms in the SOP equations are called as 1-terms and the sum terms in the POS equations are called as 0-terms.
• SOP formula is also called transient disjunctive formula whereas the POS formula is also called as transient conjuctive formula.

  Use of Transient Disjunctive (SOP) Formula :

  • Each 1-term in the transient disjunctive (SOP) formula corresponds to a path through the network that provides a 1 output.
  • From the k-map for SOP formula we can conclude that :
  • If two adjacent 1-cells on the map occur within a subcube for a single 1-term, then the output of the network must have the value 1 during the transition between the corresponding input states since only one path is involved.
  • On the other hand, if there are two adjacent 1-cells on the map which do not occur within a subcube of a single 1 term, then there has to be a path change for the 1 output of the network due to change in the value of single variable.
  • The two paths involved correspond to the two different 1-term subcubes.
  • In the process of switching from one path to the other, a momentary 0 output may occur if the original term producing a 1 output changes to zero before the term originally producing a 1 output changes to 0 before the term originally producing a 0 output changes to 1. That means a static 1 hazard exists.

  How to detect static-1 hazards ?

  We can detect static-1 hazard by plotting all the 1-terms not containing a complementary pair of literals in a transient disjunctive normal formula and then by noting if each pair of adjacent 1-cell is contained in some single subcube.

  Use of Transient Conjuctive Normal Formula (POS form) :

  • The 0-terms of the transient conjuctive normal formula or the POS formula can be used to detect the static 0-hazards.
  • A 0 term has a zero value only when each of its literals has the value 0. Therefore each 0 term corresponds to a set of input states which causes the output of a combinational circuit to be 0.
  • We can detect a static 0 hazard by mapping all the 0-terms that do not contain a pair of complementary literals and then by noting if there are any two adjacent 0s which are not contained in some single 0-term subcube (group).
  • This is clear after solving the following example.