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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