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Computing Machinery Chapter 5: Sequential Circuits.

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Presentation on theme: "Computing Machinery Chapter 5: Sequential Circuits."— Presentation transcript:

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 Diagram2. State Transition Table3. Excitation Table 4. Input/Output Expressions5. Simplification6. Circuit Diagram D 1 = (~Q 1 )Q 0 In + Q 1 Q 0 (~In) + Q 1 Q 0 In D 0 = (~Q 1 )(~Q 0 )In + (~Q 1 )Q 0 In + Q 1 (~Q 0 )In + Q 1 Q 0 In Out = Q 1 (~Q 0 )In

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

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 D 0 = (~Q 1 )(~Q 0 )In + (~Q 1 )Q 0 In + Q 1 (~Q 0 )In + Q 1 Q 0 In D 1 = (~Q 1 )Q 0 In + Q 1 Q 0 (~In) + Q 1 Q 0 In Out = Q 1 (~Q 0 )In Now we need logical expressions for D0, D1, and Out. These are extracted from the corresponding rows of the excitation table.

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 D 1 = Q 1 Q 0 + Q 0 In D 0 = In Out = Q 1 (~Q 0 )In The simplified expressions represent the combinational circuits used to apply the necessary logical values to the Q 0 and Q 0 inputs of the flip-flops and the form of the output function, Out.


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