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Computing Machinery Chapter 5: Sequential Circuits

Learn the six steps to total consciousness in designing a sequential circuit that recognizes the bit sequence "1101" within a binary sequence. Includes State Transition Diagram, Excitation Table, and Circuit Design.

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Computing Machinery Chapter 5: Sequential Circuits

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  1. Computing Machinery Chapter 5: Sequential Circuits

  2. Generic Sequential Circuit

  3. Unstable Sequential Circuits oscillators

  4. Monostable Sequential Circuit

  5. Set-Reset Latch NOR-Version

  6. Set-Reset Latch NAND-Version

  7. Synchronous (Clocked) S-R Latch

  8. Data (D-Type) Latch from S-R Latch

  9. Flip Flops

  10. J-K Flip Flop

  11. Toggle (T-Type) Flip Flop

  12. Data Register

  13. Register Transfer

  14. Shift Register

  15. Memory Unit

  16. Sequential Circuit Design the six steps to total consciousness 1. State Transition Diagram 2. State Transition Table 3. Excitation Table D1 = (~Q1)Q0In + Q1Q0(~In) + Q1Q0In D0 = (~Q1)(~Q0)In + (~Q1)Q0In + Q1(~Q0)In + Q1Q0In Out = Q1(~Q0)In 4. Input/Output Expressions 5. Simplification 6. Circuit Diagram

  17. sequential circuit 1101 bit sequence recognizer 11001010110100 00000010000000 Sequential Circuit Design Example Problem Design a sequential circuit that recognizes the bit sequence "1101" occuring in a binary sequence.

  18. Step 1: State Transition Diagram The state transistion diagram is for sequential circuit design is a Mealy Machine. The states are labeled with binary encoded values. The number of bits in the state labels is equal to the number of flip-flops in the circuit. Since this diagram has four states, they can be uniquely labeled using 2-bit binary values. This diagram represents a machine that recognizes the bit string "1101" with overlap (as read left to right).

  19. Step 2: State Transistion Table Each transition (arrow) of the state transition diagram represents a row in the state transition table. The table includes columns for the current state (time t=0), the future state (t=1), the bit string input (In), and the output (Out).

  20. Step 3: Excitation Table The excitation table gives the values needed at the inputs of the flip-flops in order to produce the correct transition when the clock pulse is applied. For the D-type flip-flop the input is set to the desired output.

  21. Step 4: Input/Output Expressions Now we need logical expressions for D0, D1, and Out. These are extracted from the corresponding rows of the excitation table. D0 = (~Q1)(~Q0)In + (~Q1)Q0In + Q1(~Q0)In + Q1Q0In D1 = (~Q1)Q0In + Q1Q0(~In) + Q1Q0In Out = Q1(~Q0)In

  22. Step 5: Simplification The logical expressions from Step 4 need to be simplified. This is accomplished using K-maps or some other method.

  23. Step 6: Circuit Design D1 = Q1Q0 + Q0In D0 = In Out = Q1(~Q0)In The simplified expressions represent the combinational circuits used to apply the necessary logical values to the Q0 and Q0 inputs of the flip-flops and the form of the output function, Out.

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