Sequential Circuits
A sequential circuit is comprised of a combinational circuit of logic gates, a clock input, and flip-flops. The combinational circuit receives input from an external source and from the flip-flops. The flip-flops receive their input from the combinational circuit. Transition between flip-flop states is induced by a signal from the clock. They in turn produce external output and, output to the combinational circuit. The output of the sequential circuit then is determined by the state of the flip-flops as well as the external inputs to the circuit.
A sequential circuit is specified by a time sequence of external inputs, external outputs and internal flip-flop binary states. Sequential circuit specifications can be represented by a state table showing output and next state as a function of input and present state. The values of the next state depend on the present state and the external inputs. The circuit output is comprised of next state and output signals and is determined by a Boolean expression relating the state of the flip-flops and external input.
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Present State |
Input |
Next State |
Output |
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|
A |
B |
x |
A |
B |
y |
|
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
0 |
1 |
0 |
|
0 |
1 |
0 |
0 |
0 |
1 |
|
0 |
1 |
1 |
1 |
1 |
0 |
|
1 |
0 |
0 |
0 |
0 |
1 |
|
1 |
0 |
1 |
1 |
0 |
0 |
|
1 |
1 |
0 |
0 |
0 |
1 |
|
1 |
1 |
1 |
1 |
0 |
0 |
Flip-flop Input Equations are Boolean expressions describing the input from the combinational circuit to the flip-flops. By examining the circuit we can derive the equations. We could also use the flip-flop excitation tables to determine the flip-flop inputs needed to achieve the present-to-next state transitions. This allows us to determine the required input from the combinational circuit to each flip-flop. Karnaugh maps based on combinational circuit input with the flip-flop excitations for output are used to find the equations and circuit diagram based on the type of flip-flop you decide to excite:
|
Present State |
Input |
Next State |
Output |
Flip-flop inputs |
A\ |
Bx |
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|
A |
B |
x |
A |
B |
y |
JA |
KA |
JB |
KB |
0 |
1 |
|
|||
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
X |
0 |
X |
1 |
X |
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|
0 |
0 |
1 |
0 |
1 |
0 |
0 |
X |
1 |
X |
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0 |
1 |
0 |
0 |
0 |
1 |
0 |
X |
X |
1 |
0 |
X |
X |
|
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|
0 |
1 |
1 |
1 |
1 |
0 |
1 |
X |
X |
0 |
1 |
1 |
1 |
|||
|
1 |
0 |
0 |
0 |
0 |
1 |
X |
1 |
0 |
X |
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|
1 |
0 |
1 |
1 |
0 |
0 |
X |
0 |
0 |
X |
0 |
1 |
X |
|
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|
1 |
1 |
0 |
0 |
0 |
1 |
X |
1 |
X |
1 |
1 |
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|
1 |
1 |
1 |
1 |
0 |
0 |
X |
0 |
X |
1 |
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combinational circuit input |
combinational circuit output |
0 |
1 |
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1 |
X |
X |
1 |
1 |
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0 |
1 |
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|
1 |
1 |
1 |
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Find the input equations for each flip-flop and the output of this circuit. Use the table to test your equations. Notation for the flip-flops next state includes their type and the name of the flip-flop in subscript.
JA = Bx, KA = x'
JB = A'x, KB = A + Bx'
Y= Ax' + Bx'
A state diagram representing this data is a directional graph comprised of nodes for each possible state of the flip-flops, connected by directed edges. These edges point to the next state of the flip-flops given the current inputs and are labeled with the binary input/output values.
The state diagrams and state tables provide different ways to represent the same data. A state table is easier to derive from a circuit diagram and a state diagram is simple to derive from the table. In circuit design a description of the desired circuit behavior is translated into a state diagram and state table. A logic diagram for the circuit exhibiting the desired behavior is then derived from this data.
by Karen Collins