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notes-326-set11

# notes-326-set11 - Sequential Circuit Design Objectives This...

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1 1 Elec 326 Sequential Circuit Design Sequential Circuit Design ± Objectives This section deals with the design of sequential circuits including the following: ² A discussion of the construction of state/output tables or diagrams from a word description or flow chart specification of sequential behavior ² A formal synthesis technique for realizing state tables and diagrams ² A less formal technique based on transition equations ± Reading Assignment ² Sections 3.3 and 3.4 . 2 Elec 326 Sequential Circuit Design 1. State Table/Diagram Specification ± There is no algorithmic way to construct the state table from a word description of the circuit. Instead, we provide a few examples to illustrate the technique. ± It is convenient to group sequential circuits as to whether the ² generate sequences, ² detect sequences, or ² transform sequences

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2 3 Elec 326 Sequential Circuit Design ± Sequence Generation: ² Example: An up/down mod 6 counter: Six states and two inputs X & Y. The inputs have the following effect: XY = 00: Do nothing (no state changes) XY = 01: Count up XY = 11: Reset to state 0 XY = 10: Count down 00 01 11 10 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 0 0 0 0 0 0 1 2 3 4 5 4 Elec 326 Sequential Circuit Design ± Example: An arbitrary sequence generator 01 0 1 2 3 4 5 6 7 Q X Q* Y 2 Y 1 Y 0 0 1 2 3 4 0 5 6 7 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0
3 5 Elec 326 Sequential Circuit Design 1 0 ± Sequence detection ² Example: Detect an even number of 1s ² Example: Detect 00110 1 0 ODD 0 EVEN 1 0 0 00 0 001 0 0011 0 ACC 1 ST 0 0 0110 REJ 0 6 Elec 326 Sequential Circuit Design ² Alternative Solution 0 1 0 0 1 1 0 1

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4 7 Elec 326 Sequential Circuit Design ± Example: Universal length 4 sequence detector ² This one detects 1011 or 0101 or 0001 or 0111 ³ Sequence transformation ± Serial binary adder (arbitrary length operands) 0 1 00/0 01/1 10/1 01/0 10/0 11/1 11/0 00/1 8 Elec 326 Sequential Circuit Design 2. Formal Sequential Circuit Synthesis ³ Summary of Design Steps ± Assign state vectors to states; the state assignment problem ± Construct the transition table ± Pick a flip-flop type for each state variable and use the flip- flop’s application tables to construct an excitation table ± Derive excitation and output equations from the excitation table. ± Construct a logic diagram from the excitation and output equations.
5 9 Elec 326 Sequential Circuit Design ± State Assignment ² Any assignment of log 2 n state variables will work, but different ones can give radically different circuits. ³ Example: mod 6 counter 0 1 2 5 4 4 11 1 1 1 1 00 0 0 0 0 10 Elec 326 Sequential Circuit Design ² Number of possible state assignments: ³ Assume we have k bits to encode n states (of course k log 2 n ). Then we have m = 2 k possible state vectors. ³ The number of ways to pick n of the m state vectors to encode the states is given by ³ Given m state vectors, we can pick any one for the first state, any one of the remaining m-1 for the second state, etc. In general we can assign the m state vectors to states in m! ways.

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notes-326-set11 - Sequential Circuit Design Objectives This...

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