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Fundamentals of Computer Science

Sequential Circuits

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What is a Sequential Circuit? • A sequential circuit consists of logic gates whose

output(s) at any time are based on the values of external input(s) and internally generated input(s).

• Sequential circuits are used to implement storage elements.

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What is a Sequential Circuit?

• Sequential circuits are generally part of a larger circuit that contains combinational circuitry as well.

• There are two types of sequential circuits– Synchronous sequential circuits can only be affected at

discrete instances of time. They are driven by clock generators. When a clock pulse is absent, the circuit cannot change.

– Asynchronous sequential circuits can be affected at any instances of time. They are not clock driven.

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Synchronous Sequential Circuits

• Flip-flops are a type of synchronous sequential circuit.

• Each flip-flop can store 1-bit of data.

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Asynchronous Sequential Circuits

• Latches are a type sequential circuit that may be asynchronous or synchronous.

• Each latch can store 1-bit of data.

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Unstable Asynchronous Sequential Circuit

• This is an example of a simplest-case sequential circuit.– The circuit is built from a single inverter.

– The output oscillates rapidly between 0 and 1.

– The circuit is essentially useless.

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Stable Asynchronous Sequential Circuits

• When the circuit settles down, the two outputs will be the complement of each other.

• There is no way to modify the value stored in the circuit.

• The circuit is essentially useless.

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Latches

• Latches are the most basic storage element.• Latches are used to build flip-flops.• This SR latch is a type of asynchronous sequential

circuit.

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Logic Simulation of SR Latch Behavior

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SR Latch with NAND GatesThe input signals for the NAND latch are the complement of the signals for the NOR latch, hence the name SR latch.

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SR Latch with Control Input• Latch can only change when C = 1, all other times the circuit

remains in the same state no matter what values are on the S and R inputs.

• This SR latch is a type of synchronous sequential circuit.

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D Latch with Control InputThe D latch is designed to eliminate the undefined state by ensuring that the S and R inputs are never high at the same time.

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Flip Flops• A latch is transparent.

– Its input value can be seen directly from its output value. Which is to say that the outputs respond immediately to the inputs.

– This is the case with the D latch when its control, C, is high.

• Flip-flops avoid the transparency problem by providing a “disconnect” between the inputs to the flip-flop and the outputs from the flip-flop.

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Flip Flops• Imagine the following scenario.

– The clock goes high.

– The output of the D latch, Q, responds to the input, D.

– Before the clock goes low, the new value of Q filters through the combinational circuit and into the D latch changing the value of Q for the second time during the same clock cycle.

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SR Master-Slave Flip-Flop• A flip-flop contains two clock-driven latches.

– The first flip-flop is the master.– The second flip-flop is the slave.

• The slave receives the inverse of the clock signal received by the master.

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SR Master-Slave Flip-Flop• When the master’s clock input is high (and

the slave’s is low) the slave is impervious to change so the slave’s outputs become stable.

• When the master’s clock is low (and the slave’s is high) the slave will respond to the master’s outputs.– During this time the master’s outputs will remain

stable since the master’s clock is low.

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Logic Simulation of SR Master-Slave Flip-Flop

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JK Master-Slave Flip-Flop• The master-slave JK flip-flop is designed to

eliminate the undefined condition (both S and R are high) found in SR latches.

• When both J and K are high, the value of the flip-flop toggles.

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Flip-Flop Characteristic Tables

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Base 4 Binary Counter with Enable• A base 4 binary counter with enable

repeatedly outputs the bit pattern 00, 01, 10, 11 when ever the enable line is high.– Since the circuit is clock driven (synchronous),

the count will change when ever the clock goes from high to low.

– When the enable line is low, the counter stops counting and the output value remain constant.

• The counter must “remember” what the current count is so that it knows what value to output next.

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Base 4 Binary Counter with Enable• The next state of the circuit is based on the

current state and the value of the enable line.– The current state of the counter is stored in two

flip-flops, one per binary digit.

• A state table is used to show what the next state of the circuit will be relative to the current state and any external inputs.– State tables are used in sequential circuit design

much as truth tables are used in combinational circuit design.

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Base 4 Binary Counter with Enable

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Base 4 Binary Counter with Enable