Sequential Circuits

Circuits that rely on past signals are known as sequential circuits

• Synchronous: behaviour can change only at discrete instances in time
• Asynchronous: behaviour can change at any instance in time

• A state diagram is a directed graph, consisting of nodes and arcs
  • Nodes represent circuit states
  • Arcs represent transitions between states

A state table (aka transition table) describes the behaviour of a sequential circuit in tabular form

A state table with the states labelled as numbers rather than letters

An excitation table shows the minimum inputs that are necessary to generate a particular next state (i.e to "excite" it to the next state 😏) when the current state is known.

Excitation table for a D flip-flop:

State assignment using the same number of state variables as there are states, with only one variable being in one state. This reduces combinational logic by increasing the number of flip-flops.

Two states are said to be equivalent if the following are true:

1. For each input, the states give the exact same output
2. For each input, the states give the same or equivalent next state

Two states and are said to be compatible if there are no state conflicts for any input valuation.

That is, and are compatible if the following hold:

1. Both and must have the same output
2. For each input valuation, one of the following conditions must be true:
   1. Both and have the same successor, OR
   2. Both and are stable, OR
   3. The successor of at least one of or is unspecified

The output (Z) depends only on the current state

In a Moore machine, the output changes synchronously with the clock (at the clock edges)

The output (Z) depends on the current state and the input.

In a Mealy machine, the output changes asynchronously with the clock (i.e output can change at any time)