(a) What is the minimum number of bits required to store each binary string of l
ID: 3841376 • Letter: #
Question
(a) What is the minimum number of bits required to store each binary string of length 50? (b) What is the minimum number of bits required to store each number with 9 base ten digits? (c) What is the minimum number of bits required to store each length 10 fixed-density binary string with 4 ones? (d) In terms of n, what is the minimum number of bits required to store each subset of a set with n elements? (e) What is the minimum number of bits required to store each rearrangement of the numbers 1 through 8? (f) What is the minimum number of bits required to store each three-letter string? (26 alphabetical letters, not case-sensitive)Explanation / Answer
(a) What is the minimum number of bits required to store each binary string of length 50?
Solution:
String of length is 50 .
Calculate number of bits is required to hold an integer , then m is an integer have n bits it will available in the range of 2^(b-1) m (2^b) -1
Consider b = 6 then
Case 1:
2^(b-1) = 2^(6-1)
= 2^(5)
= 32
Case 2:
(2^b) -1 = (2^6)-1
= 64 -1
= 63
Thus 32 50 63.
The minimum number of bits required to store each binary string of length 50 is 6 bits
(d) In terms of n, what is the minimum number of bits required to store each subset of a set with n elements?
Solution:
In terms of n, the minimum number of bits required to store each subset of set with n elements would be 2^n.
Due to the reason in binary system the minimum number of bits can be represented using the power of 2.
Thus the minimum number of bits is 2^n
(f) What is the minimum number of bits required to store each three-letter string? (26 alphabetical letters, not case-sensitive?
Solution:
Consider A is the minimum value as per the ASCII format.
ASCII Value of the A = 01000001
Character should need to have minimium of 8 bits.
Thus the minimum number of bits required to store each three letter string = 3 * 8
= 24 bits
Thus Minimum number of bits required to store each three letter string = 24 bits
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