Computer Science 150 Homework Assignment 6
Spring 1997 Solutions



1. A two-button electrical lock will actuate according to the following sequence:  A: 0 1 1 1 1 0 1 
B: 0 0 1 0 1 1 1 
Z: 0 0 0 0 0 0 1 

Z=1 opens the lock and is the circuit output while A and B correspond to the two buttons. A switch being depressed (pushed and held down) corresponds to a 1 and a switch being released (removing one’s finger from the button) corresponds to a zero. Releasing both buttons clears the circuit and only one button may be pressed or released at a time, as is the case in the above sequence. 
(a) Obtain a primitive flow table for the circuit. [20] 
STATE  NS (IN=AB) 
00  01  11  10 
A(00)  A 
B(00,10)  -   B 
C(00,10,11)  C 
D(00,10,11,10)  D 
E(00,10,11,10,11)  E 
F(00,10,11,10,11,01)  F 
G(00,10,11,10,11,01,11)  G 
H(01)  H 
I(11)  I 
J(10)  J 

(b) Obtain a reduced, merged flow table by eliminating any redundant states and by merging equivalent states. Show your merger diagram. [20] 

No reductions are possible (no rows with stable states in the same column can be combined).

Merger Diagram:

 
Merged, Reduced Flow Table:
STATE  NS (IN=AB) 
00  01  11  10 
A(00 / 00,01)  A  A 
C(00,10,11)  C 
D(00,10,11,10)  D 
E(00,10,11,10,11)  E 
F(00,10,11,10,11,01)  F 
G(00,10,11,10,11,01,11)  G 
H(01 / 11 / 10)  H  H  H 




  
  

(2) Consider the merged flow table shown opposite: