How many distinct boolean-valued functions are there of n boolean-valued signals? Write an expression in terms of n.
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To find the number of distinct boolean-valued functions of n boolean-valued signals, we can think of each boolean signal as a variable that can either have the value 0 or 1. Since each signal can take on two different values, and there are n signals, we have a total of 2^n possible combinations.
For each combination, the function can either output 0 or 1. Therefore, for each combination of the signals, we have two possible outputs. Since there are 2^n combinations, we multiply 2 by itself n times, which gives us 2^n.
Hence, the expression for the number of distinct boolean-valued functions of n boolean-valued signals is 2^n.