Cache line size and tags: Foundations — Hinglish deep dive

5.4.4 · D1 · Hardware › Memory Hierarchy & Caches › Cache line size and tags

Is page mein assume kiya gaya hai ki aap kuch nahi jaante. Hum har word, symbol, aur picture ko build karte hain jo parent note 5.4.4 use karta hai, is tarah ke har idea uske pehle wale idea par tika ho.

0. Bit kya hota hai? (neeche ki har cheez ka atom)

Ek row of light switches ki picture socho. Har switch ek bit hai. Agar mere paas 3 switches hain, toh woh kitne alag patterns dikha sakti hain? Har switch ko independently on ya off karo:

Daayein taraf red count dekho: 3 switches se $2 \times 2 \times 2 = 8$ patterns milte hain. Generally:

Is topic ko yeh kyun chahiye. Memory address ek row of bits hi hoti hai. Cache ka poora game yeh hai: "main har kaam par kitne bits kharchoon?" — aur "yeh bits kitne patterns naam de sakte hain?" ka answer exactly $2^{n}$ hai.

1. Powers of two aur $lo g_{2}$ (switches ginne ka tarika)

Humne abhi dekha $8 = 2^{3}$ . Exponent notation $2^{n}$ ka matlab hai "2 ko $n$ baar khud se multiply karo".

$2^{0} = 1, 2^{1} = 2, 2^{2} = 4, 2^{3} = 8, 2^{6} = 64, 2^{10} = 1024$

Ab ulta sawaal. Maan lo mere paas 64 patterns hain aur main poochhta hoon: kitne switches chahiye the? Jawab 6 hai, kyunki $2^{6} = 64$ . Woh tool jo poochhe "konsa exponent yeh number deta hai?" — woh hai $lo g_{2}$ .

2. Byte, aur KiB units (switches ko group karna)

Memory sizes badi ho jaati hain, isliye hum bytes ko group karte hain:

3. Hexadecimal (lambi bit rows ka shorthand)

32-bit address ko 32 zeros aur ones ki tarah likhna bahut takleef deh hai. Hex 4 bits ko ek symbol mein pack karta hai, kyunki 4 bits $2^{4} = 16$ patterns dete hain aur hex mein exactly 16 digits hain: 0 1 2 3 4 5 6 7 8 9 A B C D E F.

0x prefix sirf flag karta hai "yeh hex hai". Toh 0x2 ka matlab value 2 hai; 0xA9 ka matlab $10 \times 16 + 9 = 169$ hai.

Is topic ko yeh kyun chahiye. Addresses parent mein har jagah hex mein dikhaye jaate hain (tag 0x2, index 0xA9). Hex sirf bit row ki rewrting hai — koi naya information nahi, bas kam characters.

2^{6} = 64

lo g_{2} 512

kya hoga, aur kyun?

9

, kyunki

2^{9} = 512

32

KiB mein kitne bytes hain?

32 \times 1024 = 32, 768

bytes, jo ki

2^{15}

hai

Hex exactly 4 bits per digit kyun pack karta hai?

Kyunki

2^{4} = 16

aur hex mein 16 digits hain (

0

–

9

A

–

F

)

Cache line kya hoti hai, ek sentence mein?

L

neighboring bytes ka ek fixed run jo memory se ek unit ki tarah saath copy hota hai

Address ke lowest bits kaun sa field hota hai, aur woh kya pick karta hai?

Offset; woh line ke andar byte pick karta hai

Line size

L

diya ho toh offset bits

b

kitne?

b = lo g_{2} L

Cache size

C

aur line size

L

diye hon (direct-mapped), toh index bits

i

kitne?

i = lo g_{2} (C / L)

N

-bit address diya ho toh tag bits

t

kitne?

t = N - i - b

Connections

5.4.01-Cache-fundamentals — hum cache kyun karte hain
5.4.02-Direct-mapped-caches — pehla cache jo in teeno fields ko directly use karta hai
3.1.04-Spatial-locality — wajah ki ek line mein bahut saare bytes hote hain
6.2.01-Virtual-memory-pages — wahi "address ko split karo" trick, pages par apply ki
Yeh foundation Hinglish mein →

Foundations — Cache line size and tags

0. Bit kya hota hai? (neeche ki har cheez ka atom)

1. Powers of two aur $lo g_{2}$ (switches ginne ka tarika)

2. Byte, aur KiB units (switches ko group karna)

3. Hexadecimal (lambi bit rows ka shorthand)

4. Memory address (badi book mein ek numbered slot)

5. Cache line / block (woh chunk jo hum copy karte hain)

6. Teen address fields (sab kuch jodna)

Prerequisite map

Equipment checklist

Connections