1. Sequential Circuits
Most digital systems like digital watches, digital phones, digital computers, digital traffic light controllers and so on require memory elements
Memory elements are digital circuits that can store and retrieve data in the form of 1's and 0's.
The output of the systems with memory depends not only on present inputs but also on what has happened in the past
SR latch is an example of memory circuits that can store one bit of information
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2. SR Latch
When SR latch is storing a 1 then its Q is 1 and when storing 0 its Q is 0
R Q
S Q’
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3. SR Latch
If SR=10 then Q=1 and the latch is storing a 1, We call this setting the Latch.
If SR =10 and we change to SR=00 then the latch will remain set with Q= 1. In other words it "remembers" to stay set
If SR=01 then Q=0 and the latch is storing a 0. We call this resetting or Clearing the latch
If SR =01 and we change to SR=00 then the latch will remain set with Q= 0.
We call the value of Q at any given time the state of the latch
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4. SR Latch
The circuit (in next slide) with NOR gates is able to do this because of the feedback from the output back to the input
Note that both Q and Q' are "brought back" and connected to the inputs of the NOR gates
If both S (set) and R (reset) are 1 an undefined state with both output equal to 0 occurs ( it means the SET and RESET commands are issuing at the same time).
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6. SR Latch
The SR latch with two cross-coupled NAND gate is shown in next slide.
By setting S to 0 the output Q will be 1 that putting the latch in the set state
If S goes to 1 the circuit remains in set state
By setting R to 0 the circuit goes to reset state and stay there even after both input returns to 1
The undefined state is when both input are 0
Because NAND latch requires 0 signal to change its state it is also called S’-R’ latch
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8. Synchronous vs. Asynchronous
The behavior of a synchronous sequential circuit depends upon the any input signal at any instant of time and order of input change. This synchronization is achieved by clock generators that provides clock pulses (see the next slide). The storage elements used in clocked sequential circuits are called flip-flops.
In asynchronous sequential circuits the storage elements are time delay devices (i.e., storage is because of their propagation delay). They implemented by feedback that may cause instability in Asynchronous circuits.
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11. D latch is designed to eliminate the indeterminate state in SR latch
by making sure that inputs S and R are never equal to 1 at the same time
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13. JKFF
The JK flip-flop is an SRFF with some additional gating logic on the inputs in which the SR=11 (undetermined condition) doesn’t exist
J is used for the set and K is used for reset
J K Q Q Q’
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14. TFF By connecting K and J we can make TFF Qt T Qt + 1 Qt
Q’t
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15. Edge-Triggered vs. Level sensitive
ET FF: Transition (output change) can happen only during clock pulse transition
Clock pulse transition can be positive clock transition or negative clock transition
Level Sensitive FF: as long as the pulse level is up or down output can change
Level sensitive clock is less favorite because depending on the duration of pulse, output may change a number of times
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17. Master-Slave FF (Edge-Trigger FF)
Is a combination of 2 FFS. The first FF is master and responds to positive level of clock
The 2nd FF is slave and responds to negative level of clock
Therefore, the final output changes only during 1 to 0 transition of clock. It means during the duration of clock pulses changes in input do not have effect on output.
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19. Analysis of Clocked Sequential Circuits
The behaviour of circuit can be described by state equation
For example for the circuit (next slide) the state equations are as the follows:
A(t+1) = A(t)x(t) + B(t)x(t)
B(t+1)= A’(t).x
y(t) = (B(t) + A(t)).x’(t)
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21. State Table
The time sequence of inputs, outputs and flip-flop states can be enumerated in a state table or transition table
In the state table the present state that shows the state of flip flops comes first. So n flip flops need n present states. The inputs, next state and output come after.
The combination of present state and inputs makes state table. Output and next state can be derived from the state equations
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22. State Table There are two types of for state tables:
Mealy Model: In this model sequential circuit or state table the outputs depends on inputs as well as states
Moor Model: Where output depends on state. For example 2-D version of state table for previous circuit. Where there are only 4 different states and for each state the next states and outputs should be found based on the given inputs.
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23. State Diagram Is the graphically representation of state table.
Each state should be circled so for example if we have n flip flops we have 2n states or n circles
Each circle should be labeled by a binary number.
By using the state table the arrows can be drawn which show changes from each state to another state.
At the top of each arrow input/output is shown
Also at the top of each arrow only input(s) can be shown. See next slide
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25. Analysis with D Flip Flop
Next slide is analysis of a D flip flop with one dimensional state table and a state diagram based on Moor Model
Note that two dimensional table state is little bit difficult when there are more inputs and will not discussed here
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27. Analysis with JKFF
Determine input equations in terms of present state and input varaiables
List binary values of each equation
Use the corresponding flip-flop characteristics table to determine the next state value in the state table
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30. Analysis with T Flip-Flops
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31. Design Procedure for Sequential Circuit
Get state diagram
Assign binary codes to states
Determine number of FFS( N FFS: 2N states)
Get FF input equations (from next state)
Get output equations (from output entries)
Simplify Equations
Draw logic diagram using DFF/logic gates
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32. Design Procedure for Sequential Circuit
For example to design a circuit that detects three or more consecutive 1’s in a string of bits coming through an input line we should follow these steps (see next slides)
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