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

Date post:	02-Jan-2016
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Memory

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