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Problem 6.1
We have a ROM that has N entries of M bits each. We are interested in using it to implement a logic
function.
(a)
How big is this ROM in bytes? Express your answer in terms of N and M.
a.
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(b)
How many bits are needed to address the ROM? Express your answer in terms of N and M.
a.
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ሺሻ
(c)
How many distinct Nvariable functions with 1bit outputs can we implement with this ROM?
Express your answer in terms of N and M.
Copied from an email to Michael:
The answer to the problem is:
ቔ
כ
ቕ
. I got this by
diving the total number of bits we have (N times M) by the number of bits it takes to
represent a single Nvariable function, 2^N. We need to floor this because it doesn't
make much sense to represent some fraction of a function.
(d)
Let N = 32 and M = 2. Can we implement an arbitrary Boolean function f of 6 variables using the
ROM and at most 4 logic gates? If so, draw the circuit. If not, why not?
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 Spring '08
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