fundamentals of computer systems - memorysedwards/classes/2012/3827-s… · ·...

Fundamentals of Computer SystemsMemory

Stephen A. Edwards

Columbia University

Spring 2012

Atari Space Race, 1973

Atari Space Race PCB

Front Back (mirrored)

Read-Only Memories: Combinational Functions

2k × nROM

A0

A1

A2

...

Ak−1

D0

D1

...

Dn−1

General ROM:2k words

n bits per word

128× 1ROM

A0

A1

A2

A3

A4

A5

A6

D

Example:Space Race ROM

column

row

Implementing ROMs

0/1

0

Z: “notconnected”

0

1

0

1

1

1

Add. Data

00 01101 11010 10011 010

2-to-4Decoder

A1A0

0 1 1

1 1 0

1 0 0

0 1 0

Wordline 00

Wordline 11

Wordline 22

Wordline 33

Bitline 0

D0

Bitline 1

D1

Bitline 2

D2

Implementing ROMs

0/1

0


0

1

0

1

1

1

Add. Data

00 01101 11010 10011 010

2-to-4Decoder

1A10A0

0 1 1

1 1 0

1 0 0

0 1 0

Wordline 00

Wordline 11

Wordline 22

Wordline 33

Bitline 0

D0

Bitline 1

D1

Bitline 2

D2

1 0 0

0

0

1

0

Implementing ROMs

0/1

0


0

1

0

1

1

1

Add. Data

00 01101 11010 10011 010

2-to-4Decoder

A1A0

0

1

2

3

D0D1D2

Implementing ROMs

0/1

0


0

1

0

1

1

1

Add. Data

00 01101 11010 10011 010

2-to-4Decoder

A1A0

0

1

2

3

D0D1D2

0 01

1

1

0

1

Atari Space Race Schematic

The 1971 DEC M792-YB Bootstrap Diode Matrix

32-word, 16-bit (64-byte) ROM diode matrix

CMOS Mask-Programmed ROMs

Add. Data

00 01101 11010 10011 010

ROM “programmed”by selectivelyconnecting drainwires

Active-highwordlines

Mask ROM Die Photo

Color PROM in Pac-Man

00 0001 0702 6603 EF04 0005 F806 EA07 6F08 0009 3F0A 000B C90C 380D AA0E AF0F F610 00...

...1F 00

A Floating Gate MOSFET

Cross section of a NOR FLASH transistor. Kawai et al., ISSCC 2008 (Renesas)

Floating Gate n-channel MOSFET

Channel

Drain Source

Floating Gate

Control GateSiO2

Floating gate uncharged; Control gate at 0V: Off


Channel

Drain Source

Floating Gate

Control GateSiO2+++++++++

−−−−−−−−+++++++++

−−−−−−−−

Floating gate uncharged; Control gate positive: On


Channel

Drain Source

Floating Gate

Control GateSiO2

−−−−

−−−−++++

++++

Floating gate negative; Control gate at 0V: Off


Channel

Drain Source

Floating Gate

Control GateSiO2++++++++

−−−−−−−

−−++

Floating gate negative; Control gate positive: Off

EPROMs and FLASH use Floating-Gate MOSFETs

Static Random-Access Memory Cell

Word line

Bit line Bit line

Layout of a 6T SRAM Cell

��

��

!� !�$%� $%�&$

'()�

��"#��

Weste and Harris. Introduction to CMOS VLSI Design.Addison-Wesley, 2010.

Intel’s 2102 SRAM, 1024 × 1 bit, 1972

2102 Block Diagram

SRAM Timing

A12A11

A2A1A0

CS2

D7D6

D1D0

......

CS1

WEOE

62648K × 8SRAM

CS1

CS2

WE

OE

Addr 1 2

Data write 1 read 2

6264 SRAM Block Diagram

CY6264-1

A1A2A3A4A5A6A7A8

I/O0

256 x 32 x 8ARRAY

INPUT BUFFER

COLUMN DECODERPOWERDOWN

I/O1

I/O2

I/O3

I/O4

I/O5

I/O6

I/O7CE1CE2WE

OE

Galaga CPU detail (Namco/Midway 1981)

Dynamic RAM Cell

Word line

Bit line

Our Old Pal, the Space Race ROM0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

means

and

means


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

The decoder or“AND plane”

In a RAM or ROM,computes everyminterm

Pattern is notprogrammable


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

The decoder or“OR plane”

One term for everyoutput

Pattern isprogrammable =the contents of theROM


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

Can we do better?

Simplifying the Space Race ROM

0 0 0 00 0 0 00 1 0 00 0 0 0

A0

A1

A2A3

0 0 0 00 0 0 01 1 0 00 0 0 0

0 0 0 00 0 0 00 1 0 00 0 1 0

0 0 0 01 0 0 00 1 1 10 0 0 1

0 0 1 01 0 0 00 0 1 00 1 0 0

0 0 0 11 1 1 10 1 1 11 0 0 0

0 1 0 00 0 0 00 1 0 00 0 0 0

1 0 0 00 0 0 00 1 0 00 0 0 0

Essential minterms mean don’t expand these

Our New PAL, the Space Race ROM0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

3210D0=3210

D1=321

D2=3210+ 3210

D3=3210+ 310+3210+ 3210

D4=3210+ 3210+3210+ 3210

D5=310+ 20+ 21+3210+ 3210

D6=3210+ 3210

D7=3210+ 3210

Saved two ANDs


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

3210

321D0=3210

D1=321

D2=3210+ 3210

D3=3210+ 310+3210+ 3210

D4=3210+ 3210+3210+ 3210

D5=310+ 20+ 21+3210+ 3210

D6=3210+ 3210

D7=3210+ 3210

Saved two ANDs


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

3210

321

3210

D0=3210

D1=321

D2=3210+ 3210

D3=3210+ 310+3210+ 3210

D4=3210+ 3210+3210+ 3210

D5=310+ 20+ 21+3210+ 3210

D6=3210+ 3210

D7=3210+ 3210

Saved two ANDs


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

3210

321

3210

3210

310

3210

D0=3210

D1=321

D2=3210+ 3210

D3=3210+ 310+3210+ 3210

D4=3210+ 3210+3210+ 3210

D5=310+ 20+ 21+3210+ 3210

D6=3210+ 3210

D7=3210+ 3210

Saved two ANDs


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

3210

321

3210

3210

310

3210

3210

3210

D0=3210

D1=321

D2=3210+ 3210

D3=3210+ 310+3210+ 3210

D4=3210+ 3210+3210+ 3210

D5=310+ 20+ 21+3210+ 3210

D6=3210+ 3210

D7=3210+ 3210

Saved two ANDs


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

3210

321

3210

3210

310

3210

3210

3210

310

20

21

3210

D0=3210

D1=321

D2=3210+ 3210

D3=3210+ 310+3210+ 3210

D4=3210+ 3210+3210+ 3210

D5=310+ 20+ 21+3210+ 3210

D6=3210+ 3210

D7=3210+ 3210

Saved two ANDs


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

3210

321

3210

3210

310

3210

3210

3210

310

20

21

3210

3210

D0=3210

D1=321

D2=3210+ 3210

D3=3210+ 310+3210+ 3210

D4=3210+ 3210+3210+ 3210

D5=310+ 20+ 21+3210+ 3210

D6=3210+ 3210

D7=3210+ 3210

Saved two ANDs


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

A0A1A2A3 D0 D1 D2 D3 D4 D5 D6 D7

3210

321

3210

3210

310

3210

3210

3210

310

20

21

3210

3210

3210

D0=3210

D1=321

D2=3210+ 3210

D3=3210+ 310+3210+ 3210

D4=3210+ 3210+3210+ 3210

D5=310+ 20+ 21+3210+ 3210

D6=3210+ 3210

D7=3210+ 3210

Saved two ANDs

A 22V10 PAL: Programmable AND/Fixed OR0 4 8 12 16 20 24 28

Increments

FirstFuseNumbers

32 36 40

Macro-cell

R = 5809P = 5808

R = 5811P = 5810

R = 5813P = 5812

R = 5815P = 5814

R = 5817P = 5816

Asynchronous Reset

23

22

21

20

19

1

2

3

4

5

(to all registers)

396

0

440

880

924

1452

1496

2112

2156

2860

I/O/Q

I/O/Q

I/O/Q

I/O/Q

I/O/Q

I

I

I

I

CLK/I

Macro-cell

Macro-cell

Macro-cell

Macro-cell

Field-Programmable Gate Arrays (FPGAs)

Switch BlockLE LE LE

SB SB

LE LE LE

LUT

16×1 RAMprogrammable switch

Switch Box: 6programmable

switches

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