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) ?

Question

Laurel

Engineering

21 October, 19:46

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) ?

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Answers (1)

Know the Answer?

Breanna Pratt · Answer 1

a. 10bits

b. 7 bits

c. 6 bits

Explanation:

a. for 0 to 512

# of numbers = 512 - 0 + 1 = 513

[log ₂513] = 9 bits

we actually need 10 bits

b. for 0 to 75

# of numbers = 75 - 0 + 1 = 76

[log ₂76] = 6 bits

we actually need 7 bits

c. for - 20 to 13

# of numbers = 13 - (-20) + 1 = 34

[log ₂34] = 5 bits

we actually need 6 bits