Question: Assume that an n-bit integer (represented by standard binary notation) takes any value in the range 0 to 2^n 1 with equal probability. (a)

Assume that an n-bit integer (represented by standard binary notation) takes any value in the range 0 to 2^n − 1 with equal probability.

(a) For each bit position, what is the probability of its value being 1 and what is the probability of its value being 0?

(b) What is the average number of “1” bits for an n-bit random number?

(c) What is the expected value for the position of the leftmost “1” bit? In other words, how many positions on average must we examine when moving from left to right before encountering a “1” bit? Show the appropriate summation.

Step by Step Solution

★★★★★

3.33 Rating (150 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a For each bit position what is the probability of its value being 1 and what is the probability of its value being 0 Since the nbit integer takes any ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Practical Introduction To Data Structures Questions!

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

Figure Q2 shows an impulsive acceleration having duration 0.02 seconds and maximum magnitude of 10 m/sec. 10 accn. [m/sec] 0.2 0.4 0.6 0.8 1 time [seconds] Figure Q2 a) If a single degree of freedom...

Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...

Please help me solve these Computer System problem 2.17. Please show work so that I may follow and understand. Figure 2.12 Unsigned number Section 22 Integes Representations 63 When bit in the binary...

10. Canonical Number: A graph with n vertices can be represented as an n n binary matrix which has a l in position (ij) if and only if there is an edge (vi,v) If you "unroll" this matrix (say by...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Here are definitions of sequences and trees with integer elements: type iseq = Nil | Cons of int * (unit -> iseq) type itree = Leaf of int | Branch of itree * itree (a) In an ascending sequence such...

re Regular Languages and Finite Automata (a) Let L be the set of all strings over the alphabet {a, b} that end in a and do not contain the substring bb. Describe a deterministic finite automaton...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

Current share price of Telco Inc. is $35. Analyst forecasted net profit for this company in FY2021 is $234 Million. The company has 85 million shares outstanding. Based on this data, complete the...

The adjusted trial balance for Smoky's Supplies Ltd. is presented below. Th trial balance is prepared for December 31, 2022. Accounts Payable Accounts Receivable Accumulated Depreciation- building...

PIC 1 6 F 8 7 7 A How many bit

8 Why is ethics particularly important for the marketing research industry?

Functions can oft en be implemented by compilers in-line. An in-line function is when the body of the function is copied into the program space, allowing the overhead of the function call to be...

Can we use the tail-call optimization in this function? If no, explain why not. If yes, what is the difference in the number of executed instructions in f with and without the optimization?

Right before your function f from Exercise 2.34 returns, what do we know about contents of registers $t5, $s3, $ra, and $sp? Keep in mind that we know what the entire function f looks like, but for...

True or False: The taxable estate of a decedent is the adjusted gross estate less the marital and charitable deductions. True or False: Expenses related to the administration of an estate may only be...

What is a strategic window? Using a strategic window, how does packaging matter? Please give an example of a product that uses packaging to create a competitive edge? When does it make sense to allow...

two decimal places