Understanding Sequential Circuits: From Combinational to Sequential Logic and Latches, Study notes of Digital Logic Design and Programming

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Lecture 4:

Sequential Circuits

Term Test Date

§ Term Test

ú July 3

ú 17:00-19:

ú SW

§ Assembly Test

ú In class

ú End of July

ú Details TBA

Something else to consider…

§ Computer specs use terms

like “8 GB of RAM” and

“2.2GHz processors”.

ú What do these terms mean?

RAM = Random Access Memory; 8GB = 8 billion ints

2.2 GHz = 2.2 billion clock pulses per second.

ú But what does this mean in circuitry?

How do you use circuits to store values?

What is the purpose of a clock signal?

Two kinds of circuits

§ So far, we’ve dealt with combinational

circuits:

ú Circuits where the output values are entirely

dependent and predictable from the input values.

§ Another class of circuits: sequential circuits

ú Circuits that also depend on both the inputs and

the previous state of the circuit.

Creating sequential circuits

§ Essentially, sequential

circuits are a result of

having feedback in the

circuit.

ú How is this accomplished?

ú What is the result of having

the output of a component

or circuit be connected to

its input?

Circuit

Inputs Outputs Feedback

Combinational

Circuit

Inputs Outputs

Storage

Units

Feedback

A

Q

Gate Delay Example

B A Y

A

B

Y

B A Y Ideal Considering delays time time T T+

Feedback Circuit Example (AND)

§ Some gates don’t have useful results when

outputs are fed back on inputs.

A

Q

A QT QT+ 0 0 0 0 1 0 1 0 0 1 1 1

QT and QT+

represent the values

of Q at a time T, and

a point in time

immediately after

(T+1)

Q T QT+

If A=0, QT+1 becomes 0

no matter what QT was.

What happens next for

later values of A?

QT+1 gets stuck

at 0 and cannot

change L

Feedback Examples (NAND, NOR)

§ NAND, NOR gates w/ feedback have more

interesting characteristics, which lend

themselves to storage devices.

A

Q

A

Q

§ What makes NAND and NOR feedback circuits different?

§ Unlike the AND and OR gate circuits (which get stuck),

the output QT+1 can be changed, based on A.

Feedback Example (NAND)

§ Let’s assume we set A=

ú Then, output Q will go to 1.

ú If we leave A unchanged we can

store 1 indefinitely!

§ If we set A=1, Q’s value can change, but

there’s a catch!

A

A QT QT+ 0 0 1 0 1 1 1 0 1 1 1 0

Q

What happens

in these last

two scenarios?

Unsteady state! Can’t store 0 long!

Feedback Example (NOR)

§ Let’s assume we set A=

§ Then, output Q will go to 0.

§ If we leave A unchanged we

can store 0 indefinitely!

§ If we flip A, we can change Q, but there’s a

catch here too!

A QT QT+ 0 0 1 0 1 0 1 0 0 1 1 0

A

Q

Feedback behaviour

§ NAND behaviour § NOR behaviour A QT QT+ 0 0 1 0 1 1 1 0 1 1 1 0 A QT QT+ 0 0 1 0 1 0 1 0 0 1 1 0 § Output Q T+ can be changed, based on A. § However, gates like these that feed back on themselves could enter an unsteady state.

Latches

§ If multiple gates of these types are combined,

you can get more steady behaviour.

§ These circuits are called latches.

A

Q

B

Q

A

Q

B

Q

SR latch

§ Let’s see what happens

when the input values

are changed…

ú Assume that S and R are set

to 1 and 0 to start.

ú The R input sets the output Q

to 1 , which sets the output Q

to 0.

ú Setting R to 1 keeps the

output value Q at 1 , which

maintains both output

values.

S

Q

R

Q

1 0 0 1 0 1

S

Q

R

Q

1 0 0 1 1