Foundations — Network-on-Chip (NoC) topologies

6.3.6 · D1 · Hardware › Interconnects, Buses & SoC › Network-on-Chip (NoC) topologies

Isse pehle ki tum topic note mein koi formula padho, tumhe vocabulary chahiye. Ye page har symbol, word, aur picture define karta hai jis par parent rely karta hai — bilkul zero se shuru karke.

0. Do building blocks: node aur link

Network-on-Chip mein har cheez bilkul do cheezon se bani hai.

Figure dekho: kaale circles nodes hain, unke beech kaali lines links hain, aur jo overall pattern banta hai wo topology hai. Poora baaki topic bas itna hi hai — "hum in dots aur lines ko kaise arrange karte hain?"

1. Nodes count karna: $N$ aur $M$

Picture: dots count karo. Bas itna hi. $N$ aur $M$ kabhi mysterious nahi hote — ye wo circles hain jo tum dekh sakte ho.

Topic ko iske liye kyun zaroorat hai: har formula (diameter, bandwidth) $N$ ke terms mein likha hota hai, kyunki hum jaanna chahte hain jab hum zyada cores add karte hain to network kaise behave karta hai. $N$ mein ek formula future batata hai — 64 ya 256 cores pe kya hoga.

2. Ek hop, aur "distance" ki picture

Figure mein red path top-left node se bottom-right node tak 4 hops mein jaata hai. Har red segment exactly ek hop hai. Chip pe distance millimetres mein nahi — hops mein measure hoti hai, kyunki har hop mein ek router jitni delay lagti hai.

3. Diameter $D$ — worst-case trip

Ab hum pehla real metric define kar sakte hain.

Picture: sabse awkward corner pe khade ho, sabse awkward opposite corner tak shortest route chalke jao, aur hops count karo. Wo count $D$ hai.

Chalte hain isko grid ke liye concrete banate hain, taaki tum exactly dekh sako ki parent ka mesh formula kahan se aata hai.

4. Degree — junction pe kitni roads milti hain

Figure mein beech ka red node degree 4 hai (North, South, East, West roads). Edge pe wala node kam roads rakhta hai, isliye lower degree.

5. Bisection bandwidth $B_b$ — ek cut ke paas traffic

Ye wo metric hai jise log sabse zyada galat samajhte hain, isliye hum ise dheere dheere build karte hain.

Figure mein red dashed line grid ko beech se cut karti hai. Sirf wo links jo ise cross karte hain (4 hain) left half aur right half ke beech traffic carry kar sakte hain. Agar dono halves ek doosre se full blast baat karna chahein, saara traffic un kuch links se squeeze hoga.

6. Link bandwidth $B_{\text{link}}$ — aur $f\cdot w$ kahan se aata hai

Har $B_b$ formula "(links crossing ki sankhya) $\times B_{\text{link}}$" ke roop mein likha hota hai. To $B_{\text{link}}$ kya hai?

7. Parent jo special symbols use karta hai

Formulas mein kuch maths notation ke pieces hain. Ye raha har ek, zero se.

7.1 Floor bracket $\lfloor \rfloor$

Topic ko iske liye kyun zaroorat hai: hops whole numbers hote hain — aadha hop nahi ho sakta. Ring ka diameter $\lfloor N/2\rfloor$ kehta hai "zyada se zyada aadha chakkar, neeche rounded." $N=8$ ke liye, $\lfloor 8/2\rfloor =4$ hops.

7.2 Logarithm ${\log }_{2}N$

7.3 XOR symbol $\oplus$ aur binary bits

7.4 Big-O notation $O(\cdot )$

Topic ko iske liye kyun zaroorat hai: comparison table $O(\cdot )$ use karta hai taaki tum ek nazar mein topologies compare kar sako bina koi specific $N$ choose kiye. Ye jawaab deta hai "kaunsi topology bahut bade chips pe jeetegi?" — ye System-on-Chip (SoC) Design scaling ka theme hai.

Prerequisite map

Ise top-to-bottom padho: do atoms (node, link) har metric ko feed karte hain, metrics aur maths notation formulas ko feed karte hain, aur formulas parent topic hain. Power aur coherence downstream hain — dekho Power Management in SoCs aur Cache Coherence Protocols.

Equipment checklist

Answers cover karo; jab tum har ek bol sako tab ready ho.