If the state machine described in the figure should have a stable state, the restriction on the inputs is given by (The state machine has two inputs a and b, with transitions: (a=0)/(set 1) -> (b=0)/(set 1) -> (b=1)/(set 2), and stable state requiring both a and b to not change simultaneously) A. a.b = 1 B. a + b = 1 C. B + 1 = 0 D. a.b_bar = 1 E. a_bar + b_bar = 1

GATE 1993 · Digital Logic · Circuit Output · medium

Answer: The restriction on the inputs is a + b = 1 (Option B).

1. Identify transition conditions from the state machine figure: In the state machine shown, the machine transitions between states based on the values of a and b. When a=0 and b=0, the machine loops (unstable). When a=1 and b=1 simultaneously, the state machine also creates an oscillation condition. The only stable transitions occur when exactly the condition a+b=1 is satisfied.
2. Determine the restriction for stable state: For the machine to have a stable state: if a=0 and b=1 or a=1 and b=0 (i.e., a+b=1), the machine settles into a stable configuration. If a=b=0, no stable state exists. If a=b=1, oscillation or race condition occurs. Therefore the restriction is a+b=1.