Bit strings help required Bit-stringsLet B, = {0, 1}®n denote the set of bit-strings of length n. Then |Bn] = 2". Let 1

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Bit-strings Let B, = {0, 1}®n denote the set of bit-strings of length n. Then |Bn] = 2". Let 1

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Bit strings help required

Bit-strings
Let B, = {0, 1}®n denote the set of bit-strings of length n. Then |Bn] = 2". Let 1<t<n be some given
integer.
1. Let 1<j<n. We now construct a subset A; of Bn and count its size. Let A; be the set of bit-strings in
B, that simultancously satisfy all of the following three constraints: (i) bit j is 1, (ii) bits j +1 through
n are all 0, and (iii) among bits 1 through j – 1 there are exactly t – 1 bits that are 1. What is |A;|?
Justify your answer and show your calculations. (Hint: The answer is a binomial.)
2. The following binomial identity is truc:
() -EC )
b - 1
а — 1
b=1
Use your answer from the previous question to give a combinatorial proof of the identity. You are required
to use your answer to the previous question as a main part of your proof, and you are required to give a
combinatorial proof (as e.g. discussed in L13).

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