Module 7 — Memory Hierarchy & Cache

The principle of locality, the memory-hierarchy pyramid, direct-mapped caches (tag / index / offset), the total-bits calculation, associativity, and virtual memory — with interactive cache tools (Final Q3, slide g).

Sections

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Locality & Hierarchy

Temporal & spatial locality, the memory-hierarchy pyramid, and hit/miss terminology.

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Direct-Mapped Cache

How a block maps to a line, the tag/index/offset address split, and the hit test — with a live address decoder.

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Total-Bits Calculation

The exact "how many total bits?" question worked step-by-step, plus a live calculator.

🗂️

Associativity

Direct-mapped vs set-associative vs fully associative, and the number-of-configurations rule.

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Virtual Memory

Pages, page tables, page faults and how virtual addresses translate to physical ones.

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Practice

Cache & memory exam problems with reveal-able solutions.

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Assignment 1 — Solved

Locality, a 256-block direct-mapped cache diagram, total bits for a 512 KB cache + address split, and why set associativity cuts the miss rate.

Quick summary

LOCALITY — why a hierarchy works:
  TEMPORAL  — a referenced item is likely referenced again soon (loops).
  SPATIAL   — items near a referenced one are likely used soon (arrays) → blocks.

MEMORY HIERARCHY: registers → cache(SRAM) → main memory(DRAM) → disk.
  Down the pyramid: bigger, slower, cheaper per bit.
  HIT = found in this level. MISS = not found, fetch from the level below.

ADDRESS SPLIT (direct-mapped, byte address):
  | TAG | INDEX | BLOCK OFFSET | BYTE OFFSET |
  block offset bits = log2(words per block) ; byte offset = 2 (4 bytes/word)
  index bits        = log2(number of cache lines)
  tag bits          = address bits − index − block offset − byte offset
  Cache line chosen = (block address) mod (number of lines).

TOTAL BITS per line = valid(1) + tag + data.  Total = lines × (1 + tag + data).

ASSOCIATIVITY:
  Direct-mapped  — 1 place per block (index).           1-way.
  Set-associative— block maps to a SET of n lines.       n-way.
  Fully associative — block goes anywhere (all tag).     no index.
  A 2^n-block cache has (n+1) configurations of associativity.

VIRTUAL MEMORY: disk backs main memory; address = virtual page # + page offset;
  a PAGE TABLE maps virtual pages → physical frames (a miss = page fault).