Overview
• Booth’s Algorithm revisited
• Computer Internal Memory
• Cache memory
Booth’s Algorithm Revisited
2’s Comp Multiplication
Booth’s Algorithm
Q-1
2’s Comp Multiplication
Booth’s Algorithm
Booth : (7) x (3)
A
Q
M
3
7
0000
0011 0
0111
-------------------1001
0011 0
0111
1100
1001 1
0111
--------------------
A <- (A - M)
Shift
1st
2nd
1110
0100 1
0111
-------------------0101
0100 1
0111
0010
1010 0
0111
--------------------
Shift
A <- (A + M)
Shift
3rd
4th
0001
0101 0
0111
--------------------
Shift
Booth : (7) x (-3)
A
Q
M
-3
7
0000
1101 0
0111
-------------------1001
1101 0
0111
1100
1110 1
0111
-------------------0011
1110 1
0111
0001
1111 0
0111
-------------------1010
1111 0
0111
1101
0111 1
0111
--------------------
A <- (A - M)
Shift
1st
A <- (A + M)
Shift
2nd
A <- (A - M)
Shift
3rd
4th
1110
1011 1
0111
--------------------
Shift
Booth : (-7) x (3)
A
Q
M
3
-7
0000
0011 0
1001
-------------------0111
0011 0
1001
0011
1001 1
1001
--------------------
A <- (A - M)
Shift
1st
2nd
0001
1100 1
1001
-------------------1010
1100 1
1001
1101
0110 0
1001
--------------------
Shift
1110
1011 0
1001
--------------------
Shift
A <- (A + M)
Shift
3rd
4th
Booth : (-7) x (-3)
A
Q
M
-3
-7
0000
1101 0
1001
-------------------0111
1101 0
1001
0011
1110 1
1001
-------------------1100
1110 1
1001
1110
0111 0
1001
-------------------0101
0111 0
1001
0010
1011 1
1001
--------------------
A <- (A - M)
Shift
1st
A <- (A + M)
Shift
2nd
A <- (A - M)
Shift
3rd
4th
0001
0101 1
1001
--------------------
Shift
Computer Memory
Characteristics of Computer Memory
• Physical Location
• Capacity
• Unit of transfer
• Access Method
• Performance
• Physical Type
• Physical Characteristics
• Organization
Memory Hierarchy - Diagram
Location of Memory
• In CPU
• Internal to processor
• External to processor (peripheral device)
Capacity of Memory
• Word Size
-The natural unit of organization
• Number of words
- or Bytes
Unit of Transfer
• If Internal
– Usually governed by data bus width
• If External
– Usually a block which is much larger than a word
Addressable Unit
• Smallest location which can be uniquely addressed
• Word internally
• Cluster on disks
Access Methods
•
Sequential
•
Direct
–
–
–
–
Start at the beginning and read through in order
Access time depends on location of data and previous location
e.g. tape
Individual blocks have unique address
Alternatively
Access is by jumping to vicinity plus sequential search
Access time depends on location and previous locatio
e.g. disk
•
Random
•
Associative
- Individual addresses identify locations exactly
e.g. RAM
- Data is located by a comparison with contents of a portion of the store
- Access time is independent of location or previous access
e.g. cache
Performance
• Access time
– Time between presenting the address and getting the valid
data
• Memory Cycle time
– Time may be required for the memory to “recover” before next
access
– Cycle time is access + read/recovery (maybe rewrite)
• Transfer Rate
– Rate at which data can be moved
Physical Types
•
Semiconductor
–
•
Magnetic
–
•
Disk & Tape
Optical
–
•
RAM (SRAM, DRAM), ROM
CD & DVD [& Magneto-optical (MO)]
Others
–
–
–
Bubble
Hologram
……
Characteristics
•
Volatility
•
Persistence (or decay)
•
Erasable
•
Power consumption
The Bottom Line
• How much?
–
Capacity
• How fast?
–
Access / Transfer Rate
• How expensive?
–
$$$$
• Power usage?
–
watts
Hierarchy List
Capacity/Speed/Expense/Power
• Registers
• Cache
• Main memory
• Disk
• Tape
Internal Memory
Semiconductor Memory Types
Today’s technology: 2 Gigabit / sq in
In R&D: 100 Gigabits / sq in
Semiconductor Memory (EPROM)
Static RAM (SRAM)
• Desired for main memory
– Basically an array of flip-flops
– Simple to interface and control
– Fast
– Relatively low density – complex
– Relatively expensive
Static RAM Model
Memory Design – 1K x 4
A[00:09] 
Addr Block Select 
  D[03:00]
Memory Design – 1K x 8
D[07:04]
D[03:00]
A[00:09] 
A[00:09] 

D[07:04]
Addr Block Select =>

D[03:00]
Addr Block Select =>
Memory Design - 2k x 8
D[07:04]
Block 00
Block 01
D[03:00]
Memory Design - 4k x 8
D[07:04]
Block 00
Block 01
Block 10
Block 11
D[03:00]
Register
22 x 3 Memory
address
word select
word WE
input bits
write
enable
address
decoder
 Multiplexor
output bits
 Multiplexor
24 x 8 Memory
?
1K X 4 SRAM (Part Number 2114N)
The implementation of 1K by 4 SRAM chips may differ. This implementation perhaps
appears overly complex. However, its interface will be the same as others.
Memory Organization
• A 16Mbit chip can be organized as 1M of 16 bit words
(likely for SRAM)
OR
• A 16Mbit chip can be organized as a 2048 x 2048 x
4bit array (likely for DRAM)
– Reduces number of address pins
• Multiplex row address and column address
• 11 pins to address (211=2048)
• Adding one more pin doubles range of values so x4 capacity
Dynamic RAM (DRAM)
• Used in main memory
– Particularly larger main memory
• Bits stored as charge in capacitors - Essentially analog device
– Charges leak
• Need refreshing even when powered
– Need refresh circuits
• Higher density than SRAM (more bits per chip)
– Less devices/bit
• Slower than SRAM
– Must refresh
• Less expensive than SRAM
– More bits per area
• Less power than SRAM
– Basically capacitors
Dynamic RAM model
Typical 16 Mb DRAM (4M x 4)
256kByte Module Organization (256K x 8)
1MByte Module Organization (1Meg x 8 bits)
Refreshing
• Refresh circuit is included on the chip
• Count through rows
• Read & Write back
• Chip must be disabled during refresh ! !
• Takes time
• Occurs asynchronously
• Slows down apparent performance
Improvements in memory
RAM – continually gets denser.
DRAM – Several improvements:
SDRAM – synchronous DRAM
DDR-SDRAM - doubles transfer speed
RDRAM – asynchronous one transfer
per clock cycle
Cache Memory
So you want fast?
• It is possible to build a computer which uses only
static RAM (large capacity of fast memory)
• This would be a very fast computer
• This would be very costly
Locality of Reference
• During the course of the execution of a program,
memory references tend to cluster
• e.g. programs -loops, nesting, …
data – strings, lists, arrays, …
Cache Memory Organization
• Cache - Small amount of fast memory
– Sits between normal main memory and CPU
– May be located on CPU chip or in system
– Objective is to make slower memory system look like fast memory.
There may be more levels of cache (L1, L2,..)
Cache operation – Overview
• CPU requests contents of memory location
• Cache is checked for this data
• If present, get from cache (fast)
• If not present, read required block from main memory to cache
• Then deliver from cache to CPU
• Cache includes tags to identify which block(s) of main memory
are in the cache
Cache Read Operation - Flowchart
Cache Design Parameters
• Size of Cache
• Size of Blocks in Cache
• Mapping Function – how to assign blocks
• Write Policy - Replacement Algorithm when blocks
need to be replaced
Size Does Matter
• Cost
– More cache is expensive
• Speed
– More cache is faster (up to a point)
– Checking cache for data takes time
Typical Cache Organization
Cache/Main Direct Caching Memory Structure
Direct Mapping Cache Organization
Direct Mapping Summary
• Each block of main memory maps to only one cache
line
– i.e. if a block is in cache, it must be in one specific place
• Address is in two parts
- Least Significant w bits identify unique word
- Most Significant s bits specify which one memory
block
• The MSBs are split into a cache line field r and a tag
of s-r (most significant)
Example Direct Mapping Function
• 16MBytes main memory
– i.e. memory address is 24 bits
- (224=16M) bytes of memory
• Cache of 64k bytes
– i.e. cache is 16k
- (214) lines of 4 bytes each
• Cache block of 4 bytes
– i.e. block is 4 bytes
- (22) bytes of data per block
Example Direct Mapping Address Structure
Tag s-r
Line or Slot r
8
•
24 bit address
•
2 bit word identifier (4 byte block)
•
22 bit block identifier
14
– 8 bit tag (=22-14)
– 14 bit slot or line
•
No two blocks in the same line have the same Tag field
•
Check contents of cache by finding line and checking Tag
Word w
2
Illustration
of Example
Direct Mapping pros & cons
• Pros:
– Simple
– Inexpensive
– ?
• Cons:
– Fixed location for given block
If a program accesses 2 blocks that map to
the same line repeatedly, cache misses are
very high
– ?
The remaining slides in this set were not covered in
class.
Comparison of improved DRAM
Conventional DRAM – 40 to 100 MB/S transfer rate?
Synchronous DRAM (SDRAM)
•
•
•
•
Access is synchronized with an external clock
Address is presented to RAM
RAM finds data (CPU waits in conventional DRAM)
Since SDRAM moves data in time with system clock, CPU knows
when data will be ready
• CPU does not have to wait, it can do something else
• Burst mode allows SDRAM to set up stream of data and fire it
out in block
• DDR-SDRAM sends data twice per clock cycle (leading & trailing
edge)
SDRAM Read Timing
SDRAM
DDR SDRAM
• SDRAM can only send data once per clock
• Double-data-rate SDRAM can send data twice per
clock cycle
– Rising edge and falling edge
RAMBUS
• Adopted by Intel for Pentium & Itanium
• Main competitor to SDRAM
• Separate bus (hence the name RAMBUS)
– maximum 12 centimeter length bus !
• Bus addresses up to 320 RDRAM chips
– at 1.6Gbps
• Asynchronous block protocol
– Precise control signal timing
– 480ns access time
RAMBUS Diagram