Computing Machinery Chapter 5: Sequential Circuits.

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Computing Machinery Chapter 5: Sequential Circuits

Generic Sequential Circuit

Unstable Sequential Circuits oscillators

Monostable Sequential Circuit

Set-Reset Latch NOR-Version

Set-Reset Latch NAND-Version

Synchronous (Clocked) S-R Latch

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

Flip Flops

J-K Flip Flop

Toggle (T-Type) Flip Flop

Data Register

Register Transfer

Shift Register

Memory Unit

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

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 1100101011010000000010000000

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).

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).

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.

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.

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

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.