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计算系统导论 题目 2.55
- Authors
- Name
- Jeffrey Wang
Q：假设一个黑箱函数，该黑箱函数是一个 m 位四进制数，输出是一位四进制数字。试问该黑箱函数有多少种可能的实现？
（提示：排列组合，对于任意一个特定输入，有 4 种可能的输出）
Lee, Dalton Wayne
2.55 part G is giving some of us a big problem. Could it perhaps be explained a little better or could we get some kind of hint?
Grady, Ryan William
In lecture 5, Prof. Lumetta talked about the total number of functions that can be created using 2, 3 and n – bit inputs meaning the total number of unique truth table outputs for a given number of inputs. Look over that part in your notes and it should be fairly straightforward to create an analogous argument for quad numbers.
A:
there are m inputs, everyone has 4 conditions*(1,2,3) so there are 4^m=I inputs.
Also there are 4 outputs for each input.
So the Answer is (4^m)^4=4^4m
if you cannot get the outcome, just try to imagine what will you get if you have n 1-digit binary code input and 1 output?
In=2^n possible
Out=2 possible
for
0,0-?
0,1-?
1,0-?
1,1-?
the output might have 2^4 C.
So after all, the answer is (2^2)^2
for m x-based 1-digit input in a black box and 1-digit x^based outcome,
there are (x^m)^x=x^xm