How many bits are needed to encode the following data?

Question

A weather station on Santa Rosa Island sends data about weather conditions once every 15 minutes. The data sent is as follows:

Temperature (0..60 degrees Celsius)
Wind speed (0..170 kph)
Wind direction (0..359 degrees from North)
Humidity (0..100%)

How many bits per hour need to be sent?

Here is my approach: 2^6 bits are needed to encode values in the range 0-60. So 6 bits are necessary to encode temperature. 8 bits are needed to encode values in the range 0-170. So 2^8 bits are necessary to encode wind speed. And so on.

Any thoughts?

Ben Grossmann · Answer 1 · 2014-09-20T05:20:05.243

1

In fact, the minimum number of bits required (per update) will be $\lceil\log_2(61)+\log_2(171 )+\log_2(360)+\log_2(101)\rceil = 29$: there is no requirement in the question that we encode each type of information using separate bits.

This is in contrast to your answer of $\lceil\log_2 61\rceil + \lceil\log_2 171\rceil + \lceil\log_2 360\rceil + \lceil\log_2 101\rceil = 30$.

edited Sep 20 '14 at 05:20

answered Sep 20 '14 at 05:14

Ben Grossmann

225,327

Are you using the "Is T greater than 30? ..." algorithm? – hjhjhj57 Sep 20 '14 at 07:11
Thank you for your reply! Your observation is excellent - separate bits are not required to encode to the data. – Brian Sep 21 '14 at 00:13

How many bits are needed to encode the following data?

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