A synchronous circuit replaces the first 1 of every maximal run of consecutive ones by 0, leaving other bits unchanged. It is a two-state Mealy machine, initially state s=0. Let b be current input, t next state, and y output. Which equations implement it?
Let s remember the preceding input bit, so t=b. The first one in a run has b=1,s=0 and must output zero; subsequent ones have b=s=1 and output one. Every zero input outputs zero. Thus y=s AND b, giving B.
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