08 Computer Memory2
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Transcript of 08 Computer Memory2
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AKT211 CAO
08 Computer Memory (2)
Ghifar
Parahyangan Catholic University
Okt 31, 2011
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Last Course Review
Computer Memory System Memory Characteristics
Memory Hierarchy
RAM Basic Technology Semiconductor
SRAM vs DRAM
Advanced RAM Organization SDRAM vs DDR-RAM
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Outline
Error CorrectionSingle error correction
Double error correction
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THE BASIC OF ERROR CORRECTION
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Semiconductor System Error
Hard Failures Permanent physical defect so that it cant reliably
store data
Stuck at 0 or 1 or switch erratically between 0and 1
Soft Error
Random, nondestructive event that alters thecontents of one or more cell without damagingthe memory
Caused by power supply problems or alphaparticles
Most modern main memory systems includelogic for both detecting and correctingerrors
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Single-bit error
Only 1 bit in data unit has changed
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Error Correcting Code (ECC) Function
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Simples form of Error Detection
Using a parity bit A bit that is added to ensure that the number of bits with the
value 1in a set of bits is even or odd
Only for detecting 1-bit error, not more, nor correcting !
E.g.: no error
E.g.: 1 bit error
A wants to transmit: 1001
A computes parity bit value : 1^0^0^1 = 0A adds parity bit and sends : 10010B receives : 10010B computes parity : 1^0^0^1 = 0B reports correct transmission after observing expected result
A wants to transmit: 1001A computes parity bit value : 1^0^0^1 = 0A adds parity bit and sends : 10010*** TRANSMISION ERROR ***B receives : 11010B computes parity : 1^1^0^1 = 1B reports incorrect transmission after observing unexpected result
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Hamming Error-Correcting Code
linear error-correcting code can detect up to d-1 bit errors
can correct (d-1)/2
d is the minimum hamming distance
between all pairs in the code words
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Hamming (7, 4) Code
encodes 4 data bits (d1, d2, d3, d4) into 7bits by adding 3 parity bits (p1, p2, p3)
single error correction
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Hamming (7,4) Example
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HAMMING ALGORITHMGENERALIZATION FOR
SINGLE ERROR CORRECTION
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Generalization of the HammingSingle Error Correction
The comparison logic receives asinput two K-bit values
A bit-by-bit comparison is done
by taking the XOR The result is called the syndrome
word
The value 0 indicates that no errorwas detected and otherwise
We can determine the position fromthat syndrome word
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Required criteria for Hamming ErrorCorrection
If the syndrome contains all 0s, noerror has been detected
If the syndrome contains one andonly one bit set to 1, then an errorhas occurred in one of the n checkbits. No correction is needed
If the syndrome contains more than
one bit set to 1, then numerical valueof the syndrome indicates theposition of the data bit in error
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SEC Step-by-Step
1. Determine how long the code(check bits) must be
2. Determine the stored position
for each bit in M data bits and Kcheck bits
3. Construct the appropriate XOR
function that match with therequired criteria
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1. Determine how long the code must be
M : number of bits in data bits K : number of bits in code bits
Because an error could occur on any
of the M data bits or K check bits, wemust have :
e.g.: for a word of 8 data bits (M=8),
we have
2K1 M + K
K=3 : 23 1 < 8 + 3
K=4 : 24 1 > 8 + 4
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2. Determine the stored position
Lets see the explanation !
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3. Construct the XOR Function
Again, lets see the explanation !
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Hamming SEC-DED Code
Nowadays, more commonly, semiconductormemory is equipped with a single-error-correcting, double-error-detecting (SEC-DED)code
Needs 1 extra parity bit that indicates whetherthe total number of 1s is even or odd
Enhances the reliability of the memory, but addsthe cost ofcomplexity
E.g. : The IBM 30xx implementations used an 8-bit SEC-
DED code for each 64 bits of data in main memory
The size is actually about 12% larger than is apparent tothe user
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Hamming SEC-DED Code (2)
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Any Question ?
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Reference
Chapter 5.2: Error Correction(Stallings, William. ComputerOrganization and Architecture,
8th
ed. Prentice Hall. 2010)
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Exercises
1. Dengan penggunaan algoritma Hamming,berapakah jumlah check bit yang dibutuhkan jikadata bit berukuran 1024-bit ?
2. Terdapat data bit sebanyak 8-bit tersimpan didalam memori yang isinya 11000010. Dengan
menggunakan algoritma Hamming, tentukan nilaicheck bit yang akan tersimpan pada memori.
3. Untuk data word 8-bit 00111001, check bit yangtersimpan adalah 0111. Anggap terjadi errorpadapembacaan memori. Ketika data bit tersebut di baca
ulang dari memori, nilai check bit yang terhitungadalah 1101. Berapakah sebenarnya nilai data bityang error?
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Week 8 Assignment
Bentuklah persamaan XOR untukmenentukan SEC code (check bit) denganmenggunakan algoritma Hamming untukdata bit berukuran 16-bit. Bagaimana hasilcheck bit apabila menerima masukan databit 0101000000111001 ? Simulasikanbagaimana algoritma Hamming dapatmengoreksi error apabila terjadi error didata bit posisi ke-5 (0101000000101001).
Jelaskan jawaban Anda selengkap-lengkapnya.
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THANK YOU