Final answer:
There are 16 different binary boolean operations, calculated using the principle that for each of the four possible input combinations, there are two possible outputs, creating a total of 2^4 unique operations.
Step-by-step explanation:
The question asks about the number of different binary boolean operations that can exist. Binary boolean operations are mathematical functions that take two boolean inputs, each of which can be either true (1) or false (0), and result in a single boolean output. There are four possible inputs combinations for such operations: (0,0), (0,1), (1,0), and (1,1), and for each combination, the output can be either 0 or 1. To determine the total number of distinct operations, we calculate 2 to the power of the number of possible outputs, which is 24 because there are four input combinations and two possible outcomes for each.
There are a total of 16 different binary boolean operations that can be created, as each of the four input combinations (independently) can result in either of the two output values. This concept is similar to the calculation of possibilities in independent situations, like flipping a coin multiple times; however, here the repetitions are based on input combinations rather than actual repetitions of the event.