Computer Science 150 Homework Assignment 7
Spring 1997 Solutions


  1. A manufacturing error results in a batch of flip-flops with cross-coupled NOR/NAND gates as shown below:




  2.  
    (a) Show a primitive flow graph for the circuit. [20] 

      Let F be the state bit, so put a buffer between the output of the NAND gate and the input of the NOR gate (only one state bit is necessary because if you cut the wire at this point, there will be no more feedback loops).  So, F* = ((A + F)' B)' = (A' F' B)'.

      Here's the flow table you get from this equation: 
      STATE(F)  NS (IN=AB)  OUTPUT(F) 
      00  01  11  10 
      0 
      1  1  1  1 

      But, for it to be a primitve flow table, we have to expand state 1 into 4 states (B,C,D,E) and let state 0 be A: 
      STATE  NS(IN=AB) 
      00  01  11  10 
      A 
      B 
      C 
      D 
      E 

      So, the primitve flow graph (which is essentially an asynchronous state transition graph looks like: 
       

    (b) Show that this device cannot be reset via its input terminals A and B. [20] 

    Once you get out of state A, you cannot get back to that state through any sequence of inputs since there is no arrow going into state A in the primitive flow graph from part (a).

  1. A sequential system is comprised of two feedback logic functions:


  2.