(a) What is the minimum number of bits required to store each binary string of l
ID: 3841810 • 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?
Answer:-
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Generally, How we can calculate the number bits required to hold an integer is as follows:-
an integer m has b bits when 2^(b-1) m (2^b) – 1
so, They have given the length of the binary string as 50.
Let b=6 then 2^(b-1)=2^(6-1)
=2^(5)
=32
(2^b)-1=(2^6)-1
=63
Thus, 32 50 63,
The minimum number of bits required to store each binary string of length 50 is 6 bits.
(c) What is the minimum number of bits required to store each length 10 fixed-density binary string with 4 ones
Answer:-
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Let us consider 10 a fixed-density binary string with 4 ones as 0000001111.
If we convert this value in decimal it's value will be 15.
and as it is the minimum number So, the minimum number of bits required to store each length 10 fixed-density binary string with 4 ones is 4 bits.
(d) In terms of n, what is the minimum number of bits required to store each subset of a set with n elements?
Answer:-
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In terms of n, the minimum number of bits required to store each subset of a set with n elements would be 2^n because in a binary system the minimum number of bits can be represented using the powers of 2.
(e) What is the minimum number of bits required to store each rearrangement of the numbers 1 through 8?
Answer:-
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In binary representation,
1-1
2-10
3-11
4-100
5-101
6-110
7-111
8-1000
so the number of bits = 1+2+2+3+3+3+3+4 =21
Thus, the minimum number of bits required to store each rearrangement of the numbers 1 through 8 is 21.
(f) What is the minimum number of bits required to store each three-letter string? (26 alphabetical letters, not case-sensitive
Answer:-
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Actually, "A" is the minimum value in as per ASCI in bits representation it's value is 01000001 and a character should need to have a minimum of 8 bits.
Thus, the minimum number of bits required to store each three-letter string is 3x8=24 bits.
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