ITPEC FE Morning October 2023 Question 14
ECC is used for error detection and correction in memory. When n+2 redundant bits are required for a data bus having a width of 2n bits, what is the number of redundant bits that are required for a data bus having a width of 128 bits?
Explanation
9 bits — write the bus width as a power of two and apply the rule n + 2.
- •128 = 27, so n = 7
- •Redundant bits: 7 + 2 = 9
This agrees with the familiar case of a 64-bit bus, 26, which needs 6 + 2 = 8 check bits, the 72-bit ECC memory word.
Answer (c)
Why not others:
- •(a) 3 — the result for n = 1, a 2-bit bus; it does not follow from 128 bits
- •(b) 8 — takes the exponent as 6, but 26 = 64: that is the answer for a 64-bit bus
- •(d) 10 — takes the exponent as 8, but 28 = 256
Key rule: When a formula is given in terms of 2n, first find n exactly (27 = 128, 210 = 1,024); ECC check bits grow only by one each time the data width doubles.
Computer Component · AI-written, may contain errors
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