If there are \(m\) input lines \(n\) output lines for a decoder that is used…
2020
If there are \(m\) input lines \(n\) output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM, then the minimum value of \(m+n\) is ________ .
Attempted by 138 students.
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Correct answer: 1034
Key idea: a decoder with m input lines has 2^m distinct outputs.
Steps:
A byte-addressable 1 KB RAM has 1024 distinct byte addresses, so the decoder must provide 1024 unique outputs.
Set 2^m ≥ 1024. Since 2^10 = 1024, the minimum integer m is 10.
Then n = 2^m = 1024, so m + n = 10 + 1024 = 1034.
Answer: 1034