Memory. The logic and arithmetic circuits we’ve seen so far have no memory. They just transform input to output. Can we make circuits that remember? Memory.

Memory

• The logic and arithmetic circuits we’ve seen so far have no memory. They just transform input to output.

• Can we make circuits that remember?

Memory

• Matt really likes Sue, but he doesn’t like changing his mind… So:

• Matt decides to go to the party if Sue decides to go OR if he (Matt) had already planned to go.

The Stubborn Guy


• Two inputs to Matt’s decision: Sue, and his own state

OR

SueMatt

FeedbackWire

He Needs Feedback (from Himself)


• If Sue decides to go...

OR

SueMatt

1

The Stubborn Guy: Feedback


• If Sue decides to go, Matt will go.

OR

SueMatt

11

1



• If Sue changes her mind…

OR

SueMatt

01

1



• If Sue changes her mind, Matt will still go!• Once he decides to go, we can’t get him to change his mind

OR

SueMatt

01

1


• Matt doesn’t like Rita

• Matt decides to go to the party if Sue decides to go OR:

• If he (Matt) had already planned to go AND Rita decides NOT to go.

Enter Rita




OR

AND

Sue

Rita

Matt

Feedback Wire

Enter Rita




OR

AND

Sue

Rita

Matt

0

0

0

0

0

1

Enter Rita




OR

AND

Sue

Rita

Matt

1

0

0

0

0

1

Enter Rita




OR

AND

Sue

Rita

Matt

1

0

1

1

1

1

Enter Rita




OR

AND

Sue

Rita

Matt

0

0

1

1

1

1

Enter Rita




OR

AND

Sue

Rita

Matt

0 – nothing changes: Sue can make Matt go, but cannot make him not go

0

1

1

1

1

Enter Rita

• Matt doesn’t like Rita (maybe together they can make him not go)



OR

AND

Sue

Rita

Matt

0

1

1

1

1

1

Enter Rita




OR

AND

Sue

Rita

Matt

0

1

1

1

1

0

Enter Rita




OR

AND

Sue

Rita

Matt

0

1

1

1

0

0

Enter Rita




OR

AND

Sue

Rita

Matt

0

1

0

1

0

0

Enter Rita




OR

AND

Sue

Rita

Matt

0

1

0

0

0

0

Enter Rita




OR

AND

Sue

Rita

Matt

0

0

0

0

0

0

Enter Rita




OR

AND

Sue

Rita

Matt

0

0

0

0

0

1

Enter Rita

- no change

What Sue and Rita Can Do

• Sue can make Matt go, but cannot make him not go

• Rita can make Matt not go, but cannot make him go

OR

AND

Set

Reset

M

• M becomes 1 if Set is turned on

• M becomes 0 if Reset is turned on

• Otherwise (if both are 0), M just remembers its value

The (SR) Flip-Flop

• M becomes 1 if Set is turned on

• M becomes 0 if Reset is turned on

• Otherwise (if both are 0), M just remembers its value

S

R

M

The Flip-Flop

D

W

M

What We Really Want

• Nothing happens unless Write = 1

• If Write = 1, then M becomes set to D

• Once Write = 0 again, M just keeps its value. (It ignores D.)

• So, to set M to a value and store it as long as desired, set D to that value, then set W to 1 and then back to 0

AND

AND


S

R

MD Write

The Data Flip-Flop

AND

AND



• Once Write = 0 again, M just keeps its value. (It ignores D.)

S

R

MD Write

The Data Flip-Flop

AND

AND

• Initially, Write = 0. Let’s say M = 1.

S

R

MD Write 0

0

0

1

Using a Data Flip-Flop

AND

AND


• First, set D to desired value, say 0.

S

R

MD Write 0

0

0

10

1


AND

AND



• Then, set Write to 1.

S

R

MD Write 1

0

1

10

1


AND

AND




• This causes M to be reset to 0.

• Note use of abstraction with regard to SR flip-flop

S

R

MD Write 1

0

1

00

1


AND

AND




• This causes M to be reset to 0.

• Finally set Write back to 0. Now D is irrelevant.

S

R

MD Write 0

0

0

0?

1


• If Write = 0, M just keeps its value. (It ignores D.)


D

Write

M

The Data Flip-Flop

Are We Done?

• When Write = 1, then M = D.

• If we have some feedback between M and D,then circuit could go haywire.

D

Write

M ??

A Subtle Problem

• For example, suppose a NOT gate connects M and D.

• When Write = 1, M and D keep changing. We have no control.

D

Write

M NOT

1

?

?

A Subtle Problem

• We want to control the feedback, so that each time we set Write to 1 and then back to 0, M stores only the last value of D

• (In this case, M should invert itself once each time we set Write to 1 and back to 0)

D

Write

M NOT

1

?

?

A Subtle Problem

D1

W1

M1D0

W0

M0

“Outer door” “Inner door”

Write

• Two-Stage System to prevent D ever passing through directly to M (W0,W1 connected by NOT, so never 1 at the same time)

D M

The “Airlock” Flip-Flop

D1

W1

M1D0

W0

M0


Write

• We start with Write = 0.

• Let’s say D is always NOT M; i.e. connected by NOT gate.Start with D = 0, M = 1.

D M


D1

W1

M1D0

W0

M0


Write

• We start with Write = 0.

• Let’s say D is always NOT M; i.e. connected by NOT gateStart with D = 0, M = 1.

D M

0

0

1

1 1


D1

W1

M1D0

W0

M0


Write

• Want to store D in memory.

• Set Write to 1

D M

1

0

0

1 1


D1

W1

M1D0

W0

M0


Write

• Want to store D in memory.

• Set Write to 1

• “Outer” flip-flop sets M0 = D0 = 0

• “Inner” flip-flop ignores D1 since W1 = 0

D M

1

0

0

0 1


D1

W1

M1D0

W0

M0


Write

• Now, set Write back to 0

D M

0

0

1

0 1


D1

W1

M1D0

W0

M0


Write

• Now, set Write back to 0

• Now “Inner” flip-flop sets M = D1 = 0

D M

0

0

1

0 0


D1

W1

M1D0

W0

M0


Write

• Because of feedback, D might change to (NOT M) , which is 1

• But Write = 0, so “Outer” flip-flop ignores D, so M0 stays 0.

D M

0

1

1

0 0


D1

W1

M1D0

W0

M0


Write

• So memory does not change until we “toggle” Write.

• (“toggle” means change from 0 to 1 or vice versa)

D M

0

1

1

0 0


D1

W1

M1D0

W0

M0


Write

• This is Real Memory!

D M


DM

W

DM

W

DM

W

DM

WWrite

Data1

Data2

Data3

Data4

Memory “Register”: 4 bits

Review

• We have used the Universal method to build– ALU

– Memory

• Next steps– State machines to computer with memory

– Building the computer

– Writing a program to use the computer

Memory. The logic and arithmetic circuits we’ve seen so far have no memory. They just transform input to output. Can we make circuits that remember? Memory.

Documents

matt doesnt

sue matt feedback

sue rita matt feedback

rita slide

feedback slide

memory slide

stubborn guy slide

arithmetic circuits