In class we learned that in order to uniquely identify one of N equally likely symbols, ceiling (〖log〗_2 N) bits of information must be communicated. Answer the questions below:

(a) How many bits are necessary to encode an integer in the range of 0 to 512 (inclusive)?
(b) It must require 10 bits at least, not 9, because 2^9 = 512, however this is inclusive so it is actually 513 numbers and therefore 10 bits. How many bits are necessary to encode an integer in the range of 0 to 75 (inclusive)?
(c) It would require at least 7 bits. 2^6 = 64 which is not enough, so it must be 2^7 = 128 bits. How many bits are necessary to encode an integer in the range of -20 to 13 (inclusive)?