LAB 13 - SEQUENTIAL CIRCUIT

What is sequential state?

Can move from this state to another, or can stay at a state for a period of time.

How many types of sequential systems there are?

2 which are:

• Mealy

• Moore

What is a Mealy FSM?

Sequential CC in which the output depends on both the inputs and the present state.

There is a carry in during the transition from this state to the next state.

What is a Moore FSM?

Sequential CC in which the output depends on only the present state.

Each state has a fixed output regardless of how you construct that.

Comparison between Moore and Mealy.

• Moore: more predictable since each state has fixed output. However, it could be slower since for 4 inputs, each input having 4 states. Therefore, we have to evaluate 16 states.

• Mealy: faster, yet it is harder to predict since the O/P is not fixed. Furthermore, a new carry bit added can affect the whole system.

What is synchronous sequential system?

A sequential system depends on a specific signal to change states, e.g: clock.

What is asynchronous sequential system?

No need to depend on signal to change state.

Whose state table is this?

Mealy.

Whose state table is this?

Moore.

In this state table of Mealy, why cell of the first row at column ‘11’ has “S1, 0”?

• x1 + x2 (1 + 1) = 0 → sum = 0 and has a carry of 1.

• Since there is a carry, the state changes from S0 to S1 (S1 is a state of having a carry to be input into the next state).

In this state table of Mealy, why cell of the second row at column ‘11’ has “S1, 1”

• x1 + x2 = 1. Yet, since there is Cout from previous state being Cin of this present state → x1 + x2 + Cin = 1 with a carry of 1.

• Since there is a carry, the state will become S1 (has a carry).

How can carry out be calculated?

(A AND B) OR (A AND Cin) OR (B AND Cin).

How is an addition performed?

A XOR B XOR Cin.

In this state table of Moore, what does “S11” stand for?

S11 has 2 digits:

• First digit ‘1’ means that there is a carry of 1.

• Second digit ‘1’ means that there is a sum of 1.

In this state table of Moore, how can a state at a column of a combination of inputs determined?

• Sum is determined by x1 XOR x2 XOR Cin. Where x1 and x2 are inputs from the corresponding column, while Cin is got from the corresponding row (PS column).

In this state table of Moore, how can output column determined?

Output column is the sum corresponding to the state in the same row at the PS column since in Moore, output is not affected by inputs but just state.

What does “bistable” means?

A logical device that has 2 stable states, which are ‘0’ and ‘1’. It can indefinitely stay in that state until you flip it.

How many output gates do a memory device has?

There are 2:

• Q: output gate.

• Q’: compliment output gate.

How many types of bistable devices are there?

There are 2:

• Flip flop: synchronous sequential system.

• Latch: asynchronous sequential system.

What is a RS Latch?

It depends on 2 inputs ‘S’ and ‘R"‘.

• S’ = 0 and R’ = 1 → set → Q = 1 and Q’ = 0.

• S’ = 1 and R’ = 0 → reset → Q = 0 and Q’ =1

• S’ = 0 and R’ = 0 → Q = 0 and Q’ = 0

• S’ = 1 and R’ = 1 → Q = latch and Q’ = latch

When happens to the outputs of RS Latch if both S and R = 0?

Q = latch and Q’ = latch.

What is a D Latch?

Characteristic equation: D = Q.

→ Output is the same as input captured.

What is a RS flip flop?

• Has 2 inputs R and S which control.

• If R = 0 → reset → Q = 0 and vice versa.

• If both R and S = 1 → forbidden state.

• If both R and S = 0 → no change.

Truth table of a RS flip flop?

What is a JK flip flop?

• Depends on J (Jack) and K (Kill)

• J = 0 → set → Q = 1 and vice versa.

• Both J, K = 0 → no change.

• Both J, K = 1 → toggle → Q = Q’ and Q’ = Q.

What is T flip flop?

• Depends on an input T.

• If T = 0 → no change.

• If T = 1 → toggle → Q = Q’ and Q’ = Q.

Truth table of a JK flip flop?

Truth table of a T flip flop?

What is a D flip flop?

• Depends on D - a source of input.

• Whenever meet a new rising edge, flip flop will capture the value of D at that current moment.

Truth table of a D flip flop?

What are those flip flops that do not depend on a synchronous signal?

D and RS

What are those flip flops that depend on a synchronous signal?

JK and T