A processor supports a maximum memory of 4 GB. The memory is word-addressable,…
2019
A processor supports a maximum memory of 4 GB. The memory is word-addressable, and each word is 2 bytes. Which option gives the minimum address-bus width sufficient to address the entire memory?
Answer: C. At least 31 bits — Concept: In a word-addressable memory, each address identifies one complete word. If a memory contains N addressable words, an n-bit address bus can identify…
- A.
At least 28 bits
- B.
At least 2 bytes
- C.
At least 31 bits
- D.
Minimum 4 bytes
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Show answer & explanation
Correct answer: C
Concept: In a word-addressable memory, each address identifies one complete word. If a memory contains N addressable words, an n-bit address bus can identify 2n addresses, so n = log2 N.
Capacity must therefore be converted into a count of words before the address width is calculated.
Application
Convert the total capacity: 4 GB = 4 × 230 bytes = 232 bytes.
Count addressable words: 232 bytes ÷ 2 bytes per word = 231 words.
Find the address width: log2(231) = 31 address bits.
Cross-check: A 31-bit bus supplies 231 word addresses. At 2 bytes per word, this covers 232 bytes, which is 4 GB under the binary memory convention.
Result: The processor needs an address bus of at least 31 bits.
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