Synchronous Sequential Circuits Chapter 5

Sequential Circuits

• A sequential circuit has two main components: combinational logic and storage elements.
• Output function: Outputs = g(Inputs, State)
• Next state function: Next State = f(Inputs, State)

Types of Sequential Circuits

• Synchronous circuits:
  • Behavior defined from knowledge of signals at discrete instances of time
  • Storage elements observe inputs and change state only in relation to a timing signal (clock pulses)
• Asynchronous circuits:
  • Behavior defined from knowledge of inputs at any instant of time and the order in which inputs change
  • If clock is regarded as another input, all circuits are asynchronous

Storage Elements: Latches

• Latches are asynchronous storage circuits
• The major difference among storage elements is in the number of inputs they possess and how they affect the binary state
• Types of latches:
  • SR Latches
  • D Latches

SR Latch

• Cross-coupling two NOR gates gives the S-R Latch
• Function diagram: Q = (R+Q')', Q' = (S+Q)'
• Truth table:
  • Q(t+1) = Q(t) if R=0 and S=0
  • Q(t+1) = 0 if R=1 and S=0
  • Q(t+1) = 1 if R=0 and S=1
  • Q(t+1) = undefined if R=1 and S=1

Problems with SR Latch

• If SR=11, both Qnext and Q'next would become 0, which contradicts the assumption that Q and Q' are always complemented
• If S=0 and R=0, the circuit enters an infinite loop where Q and Q' cycle between 0 and 1 forever

Clocked SR Latch

• Adding two NAND gates to the basic S-R latch gives the clocked S-R latch
• Has a time sequence behavior similar to the basic S-R latch except that the S and R inputs are only observed when the clock line C is high

D Latch (Transparent Latch)

• Adding an inverter to the S-R latch gives the D latch
• Note that there are no "indeterminate" states (solves the S-R latch problem)

Overview of Sequential Circuits

• Storage elements: Latches or Flip-Flops
• Introduction to sequential circuits
• Types of sequential circuits
• Storage elements: Latches, Flip-Flops
• Sequential circuit analysis: State tables, State diagrams