memory(external memory) RAID- Amira Hurriff

              RAID  by Nor Amira Hurriff (B031210233)

what is RAID ?

R- Redundant 

A- Array

I- Independent / inexpensive

D- Disks

 RAID 0

- tidak bertindan atau lebih.( tiada cermin, tiada pariti)

-data menjalur merintangi disk.

- disk dalam kedudukan selari.

-minimum 2 disk

- prestasi baik (as block striped)

- tidak boleh digunakan untuk sistem yang kritikal

A,B,C,D,E,F - gambaran sebagai Blok

RAID 1

- disk bercermin

- data dijalur merintangi disk

- setiap jalur mempunyai salinan pada disk yang berbeza

- Ditulis(write) pada kedua-dua disk.

- Mahal

-minimum 2 disk

-prestasi baik (tiada jalur,tiada pariti)

-lebihan atau tindanan yang baik( excellent redundancy) * sebab blok di cerminkan

A,B,C - BLOK.. ada 2 salinan.untuk disk 1 dan disk 2

RAID 2

-menggunakan "bit level striping" . striping disk merintangi disk.

- perlu ada 2 kumpulan disk  a) kump 1- digunakan untuk tulis data

                                             b) kump 2- menulis kod pembetulan ralat (error correction code)

-menggunakan Hamming Error Correction Code (ECC)

 dan menyimpan maklumat dalam disk bertindan(redundancy disk)

- apabila data ditulis pada disk,ia mengira kod ECC untuk data , dan menjalur data bits kepada data disk.serta menulis kod ECC kepada disk bertindan(redundancy disk)

- Bila data dibaca dari disk ,ia juga baca data dari ECC code (dari redundancy disk) dan di 'cek' sama ada data dalam keadaan konsisten.Jika perlu diubah ,ia perlu membuat pembetulan.(correction)

**raid 2 banyak memerlukan disk.dan boleh dikonfigurasikan dalam disk yang berbeza. 

** raid 2 tidak lagi digunakan sebab mahal dan rumit.selain itu, ECC menjadi lebihan dan tidak digunakan , sebab Hard disk sekarang boleh "act as ECC". :)

** b1,b2,b3,b4,b5,b6 - Bits

**E1,E2,E3,E4,E5,E6- kod pembetulan ralat (error correction code)

RAID 3

- Digunakan dalam 'striping' tahap byte

-menggunakan disk berganda . dan ada disk khas untuk menyimpan pariti

-disk harus berputar selari untuk mendapatkan data.

good performance - read and write data sequentially

bad performance- read and write randomly

- raid 3 ini jarang digunakan

** B1,B2,B3 ...B9 - bait

** P1,P2,P3 - Pariti

RAID 4

-setiap disk beroperasi secara bebas 

- baik digunakan untuk input/output yang tinggi

-mempunyai jalur yang besar

- bit per bit pariti dikira keseluruhan jalur untuk setiap disk

- pariti disimpan untuk disk pariti

** A,B,C...I - Blok

** p1,p2,p3 - pariti

RAID 5

-minimum 3 disk - good performance (sebagai blok berjalur)

                          - good redundancy ( pariti di agih dengan baik)

-pariti disk merintangi semua disk

-mengelakkan (raid 4) menjadi sesak pada pariti disk

-memperuntukkan pusingan robin untuk jalur pariti

**p1,p2,p3 - pariti

RAID 6

-sama seperti raid 5,ini bukan striping tahap blok.tetapi ia menggunakan 2 pariti .

- dalam rajah atas, pariti teragih dan tersusun

-mewujudkan 2 pariti untuk blok data

-boleh mengendalikan dua failure disk (cakera kegagalan)

- raid 6 ini rumit dalam untuk menjadi sebagai raid controller.kerana ia harus mengira 2 pariti data untuk setiap data blok.

Karnaugh Map by Eliza Joanne

The Karnaugh map or known as K-map is a simple method of minimizing Boolean expressions. K-map is a representation of the truth table in a grid-like manner.

Grouping 1’s in Karnaugh Map

• The groups only contain 1 s, no zeros allowed.
• There can only be adjacent grouping of cells only, no diagonal grouping.
• The number of groups can only be a power of 2(2ⁿ, where n = 0, 1, 2, 3, 4,…).
• The groups must be large as possible.
• All 1 must belong to a group.
• Overlapping of groups are allowed.
• Wrap around is allowed.
• There must be a few as possible groups.

In this case four variables are used, therefore the K-map has 16 outputs.

Sum-of-products (SOP)

Example 1: 

Let X = (A’B’C’D’) + (A’B’CD’) + (ABC’D’) + (ABC’D) + (AB’C’D’) + (AB’C’D)
     

                   
                  

Note: 
The labelling of 00, 01, 10, 11 is not in order. In the K-map 11 must be written before 10.

Following the rules as above:

Looking at the big box (4x4), AC’ does not change and from the wrap around A’B’D’ does not change. Hence, the simplification is AC’ + A’B’D’.

Example 2:

Let G = (A’B’C’D’) + (A’BC’D’) + (ABC’D’) + (AB’C’D’) + (AB’C’D)

                         

Following the rules as above:

Looking at the long box (1x4), C’D’ does not change and from the 2x2 box, AB’ does not change. Hence, the simplification is C’D’ + AB’C’.

 Product-of-sums (POS)

In a similar way as SOP, POS is simplified but using 0 instead of 1.

The rules of grouping 0 are the same as grouping 1. The changes are in grouping 0, no 1 can be included.

Example 1:

Let X = (A’B’C’D’) + (A’B’CD’) + (ABC’D’) + (ABC’D) + (AB’C’D’) + (AB’C’D)

Following the rules as above:

Looking at the 4x4 yellow box, AC does not change, from the green 4x4 box, A’D does not change and from the 1x4 box A’B’ does not change. Hence, the simplification is (A’+C’) x (A+D’) x (A+B).

Example 2:

Let H Let G = (A’B’C’D’) + (A’BC’D’) + (ABC’D’) + (AB’C’D’) + (AB’C’D)

                                                         

                                  

Following the rules as above:

Looking at the yellow 4x2 box, C does not change, from the green 4x4 box, BD does not change, and from the blue 4x4 box, A’D does not change. Hence, the simplification is C’ x (B’+D’) x (A+D’).

* With the known simplification the expression above can be found.

Boolean Algebra by AmiraHurriff

BOOLEAN ALGEBRA by AmiraHurriff
  Introduction :
A Boolean algebra is the combination of variables and operators.usually, it has one or more inputs and produces an output in the
Range of 0 and 1.  Laws Boolean Algebra expressions have been created to help reduce the number of logic gates(Boolean equation.
 These are consist of Boolean Algebra Laws:
•             commutative laws
•             Associative laws
•             Distributive laws
•             Identity laws
•             Zero and one laws
•             Inverse laws
•             DeMorgan’s laws

Types of law	AND form (gates)	OR form (gates)
Identity law	A . 1 = A	A + 0 = A
Zero and One law	A . 0 = 0	A + 1 = 1
Inverse law	A . A’ = 0	A + A’ = 1
Commutative law	A . B = B.A	A + B = B + A
Associative law	A.(B.C) = (A.B).C	A+(B+C)=(A + B)+C
Distributive law	A+(B.C)=(A+B).(A+C)	A.(B+C)=(A.B) + (A.C)
DeMorgan’s Law	(A’.B’)= A’ + B’	(A’ + B’)= A’.B’

 
De Morgan’s laws:
1.  Two separate terms NOR´ed together is the same as the two terms inverted (Complement) and AND´ed for example, A’+B’ = A’∙ B’.
2. Two separate terms NAND´ed together is the same as the two terms inverted (Complement) and OR´ed for example, A’∙B’ = A’ +B’.

Logic gate by sangkirthana

Logic gate

Logic gate

• A gate is digital circuit which either allow a signal pass through it or stop it.
• Its is commonly known as logic gate because it only allows the signal to pass through it only if certain logical condition is satisfied. 

Truth table and Boolean expression

• A table that shows all the possible combination of input and their corresponding output combination for logic gate is called a truth table or table of combination of that logic gate.
• George Boole device different kind of algebra called Boolean algebra deal wit logical statement  which having only 2 value namely either true or false value.
• In Boolean expression 1 denotes a truth statement and 0 denote the false statement
• The three basic operation in Boolean algebra are: 

1.  OR operation
2.  AND operation
3.  NOT operation

sum of product and product of sum by Shahariah Zulkifly

sum of product and product of sum

• logic function can be written in a canonical form
• there only 2 level of gates, AND and OR
• with a possible inversion on the final output
• sum of products represention of logical sum ( OR ) of product
• a product of sum is just there opposite
• E = ((A&B) + (A&C) + (B&C)) & (A&B&C)'
• E = (A&B&C') + (A&C&B') + (B&CA') (SOP)
• first equation has three levels of logic
• 2nd equation is in sum-of-products form