Final answer:
A binary code using eight switches has 256 different possible combinations, calculated as 2 to the power of 8.
Step-by-step explanation:
A binary code using eight switches has a total of 28 different possible combinations. In binary systems, each switch can be in one of two states: on or off, representing 1 or 0 respectively. Since there are eight independent switches, and each switch has two possible states, we use the rule of multiplication for independent events to calculate the total number of combinations. Each of the eight positions can be occupied by either a 1 or a 0, giving us 2 choices per position.
To find the total number of combinations, we raise the number of possibilities for a single switch (which is 2) to the power of the number of switches (which is 8): 28 = 256. Therefore, an eight-switch binary code can generate 256 different outcomes.