A space probe is controlled by 7 different instructions from the ground. the probabilities of sending these instructions vary - the three most common instructions have probabilities 1/2, 1/4, and 1/8 of being sent, respectively. the remaining four instructions are equally likely to be sent. in expectation, what is the minimum number of whole number bits required to communicate with the probe?

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Mathematics

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24 July, 20:51

A space probe is controlled by 7 different instructions from the ground. the probabilities of sending these instructions vary - the three most common instructions have probabilities 1/2, 1/4, and 1/8 of being sent, respectively. the remaining four instructions are equally likely to be sent. in expectation, what is the minimum number of whole number bits required to communicate with the probe?

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Amir Heath · Answer 1

The space probe needs to be able to differentiate 7 different type of command.

The possible way that can be code by n bits would be 2^n. Then, the number of bits for coding at least 7 different commands would be:

2^n > 7

2^n > 2^2.80

n > 2.80

n=3

You need at least 3 bits