A sequential circuit has one primary input m, and one primary output n. It has two D flip-flops with inputs D₂ and Do, and corresponding flip-flop outputs Q₂ and Q. It also has a T flip-flop with input T₁ and output Q₁. The circuit is wired in a way described by the following equations: D₂ = m'Q₂Q₁ +mQ₂'Q₁ + m²Q₂'Q₁'Qo' • T₁ = Q₁²Q₁ + mQ₁' + mQ₂'Q' + m²Q₂'Që + m²Q₂Q₁ Do = m'Q₂' + m'Q₁³Qỏ' + m²Q₁Q0 + mQ₂Q₁ Qo' n = Q₂Q₁ +mQ₁' + m'Q₂'Qo' Using the sequential circuit, perform state minimization by implication to reduce the number of states to a minimum. Which states are equivalent? In the minimized circuit, how many flip-flops are needed to implement the circuit?

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Latches and Flip Flop

Just like logic gates, the latches and flip-flops are the important elements of an electronic circuit. The logic gates form the important part of combinatorial circuits, while the latches and flip-flops form the essential part of a sequential circuit. Sequential circuits form the important concept of automata theory in electronics and electrical engineering, these circuits are a kind of logic circuit whose output depends on both present input and past inputs, that is, the input history.