A 4-way set-associative cache memory unit with a capacity of 16 KB is built using a block size of 8 words. The word length is 32 bits. The size of the physical address space is 4 GB. The number of bits for the TAG field is ________

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Official answer: 20

Cache Memory and Hierarchy

Physical Address Space:
$\text{Physical Address Space} = 4\text{ GB} = 2^{32}\text{ bytes}$
$\text{Physical Address} = 32\text{ bits}$
Block / Line Size:
$\text{Word length} = 32\text{ bits} = 4\text{ bytes}$
$\text{Block size} = 8\text{ words} = 8 \times 4\text{ bytes} = 32\text{ bytes} = 2^5\text{ bytes}$
$\text{Block offset} = 5\text{ bits}$
Number of Lines in Cache:
$\text{Cache size} = 16\text{ KB} = 16 \times 1024\text{ bytes} = 2^{14}\text{ bytes}$
$\text{Total lines} = \frac{2^{14}\text{ bytes}}{2^5\text{ bytes}} = 2^9 = 512\text{ lines}$
Number of Sets in Cache:
$\text{Associativity} = 4\text{-way}$
$\text{Number of sets} = \frac{512}{4} = 128 = 2^7\text{ sets}$
$\text{Set index bits} = 7\text{ bits}$
Tag Bits:
$\text{Tag bits} = \text{Physical Address bits} - (\text{Set index bits} + \text{Block offset bits})$
$\text{Tag bits} = 32 - (7 + 5) = 32 - 12 = 20\text{ bits}$

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This Cache Memory and Hierarchy previous year question is Q9 of the GATE CSE 2014 Set 2 paper. Find more GATE CSE PYQs on Cache Memory and Hierarchy in Computer Organization and Architecture, or browse all GATE CSE PYQs.

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Cache Memory and Hierarchy in GATE CSE

Cache Memory and Hierarchy has 47 GATE CSE PYQs across 23 papers from 2011 to 2026. 7 of them are 1-mark NAT questions like this one, and GATE CSE 2014 Set 2 has 4.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.