Pearson eText for Starting Out with Java: Early Objects -- Instant Access (Pearson+)
6th Edition
ISBN: 9780137516803
Author: Tony Gaddis
Publisher: PEARSON+
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Textbook Question
Chapter 14, Problem 9TF
True or False: It is not necessary to have a base case in all recursive
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2. Signed Integers
Unsigned binary numbers work for natural numbers, but many calculations use negative
numbers as well. To deal with this, a number of different methods have been used to represent
signed numbers, but we will focus on two's complement, as it is the standard solution for
representing signed integers.
2.1 Two's complement
• Most significant bit has a negative value, all others are positive. So, the value of an n-digit
-2
two's complement number can be written as: Σ2 2¹ di 2n-1 dn
• Otherwise exactly the same as unsigned integers.
i=0
-
• A neat trick for flipping the sign of a two's complement number: flip all the bits (0 becomes 1,
or 1 becomes 0) and then add 1 to the least significant bit.
• Addition is exactly the same as with an unsigned number.
2.2 Exercises
For questions 1-3, answer each one for the case of a two's complement number and an
unsigned number, indicating if it cannot be answered with a specific representation.
1. (15 pts) What is the largest integer…
can u solve this question
1. Unsigned Integers
If we have an n-digit unsigned numeral dn-1d n-2...do in radix (or base) r, then the value of that
numeral is
n−1
r² di
Σi=0
which is basically saying that instead of a 10's or 100's place we have an r's or
r²'s place. For binary, decimal, and hex r equals 2, 10, and 16, respectively.
Just a reminder that in order to write down a large number, we typically use the IEC or SI
prefixing system:
IEC: Ki = 210, Mi = 220, Gi = 230, Ti = 240, Pi = 250, Ei = 260, Zi = 270, Yi = 280;
SI: K=103, M = 106, G = 109, T = 10¹², P = 1015, E = 10¹8, Z = 1021, Y = 1024.
1.1 Conversions
a. (15 pts) Write the following using IEC prefixes: 213, 223, 251, 272, 226, 244
21323 Ki8 Ki
223 23 Mi 8 Mi
b. (15 pts) Write the following using SI prefixes: 107, 10¹7, 10¹¹, 1022, 1026, 1015
107 10¹ M = 10 M
=
1017102 P = 100 P
c. (10 pts) Write the following with powers of 10: 7 K, 100 E, 21 G
7 K = 7*10³
Chapter 14 Solutions
Pearson eText for Starting Out with Java: Early Objects -- Instant Access (Pearson+)
Ch. 14.2 - It is said that a recursive algorithm has more...Ch. 14.2 - Prob. 14.2CPCh. 14.2 - What is a recursive case?Ch. 14.2 - What causes a recursive algorithm to stop calling...Ch. 14.2 - What is direct recursion? What is indirect...Ch. 14 - Prob. 1MCCh. 14 - This is the part of a problem that can be solved...Ch. 14 - This is the part of a problem that is solved with...Ch. 14 - This is when a method explicitly calls itself. a....Ch. 14 - Prob. 5MC
Ch. 14 - Prob. 6MCCh. 14 - True or False: An iterative algorithm will usually...Ch. 14 - True or False: Some problems can be solved through...Ch. 14 - True or False: It is not necessary to have a base...Ch. 14 - True or False: In the base case, a recursive...Ch. 14 - Find the error in the following program: public...Ch. 14 - Prob. 1AWCh. 14 - Prob. 2AWCh. 14 - What will the following program display? public...Ch. 14 - Prob. 4AWCh. 14 - What will the following program display? public...Ch. 14 - Convert the following iterative method to one that...Ch. 14 - Write an iterative version (using a loop instead...Ch. 14 - What is the difference between an iterative...Ch. 14 - What is a recursive algorithms base case? What is...Ch. 14 - What is the base case of each of the recursive...Ch. 14 - What type of recursive method do you think would...Ch. 14 - Which repetition approach is less efficient: a...Ch. 14 - When recursion is used to solve a problem, why...Ch. 14 - How is a problem usually reduced with a recursive...Ch. 14 - Prob. 1PCCh. 14 - isMember Method Write a recursive boolean method...Ch. 14 - String Reverser Write a recursive method that...Ch. 14 - maxElement Method Write a method named maxElement,...Ch. 14 - Palindrome Detector A palindrome is any word,...Ch. 14 - Character Counter Write a method that uses...Ch. 14 - Recursive Power Method Write a method that uses...Ch. 14 - Sum of Numbers Write a method that accepts an...Ch. 14 - Ackermarms Function Ackermanns function is a...Ch. 14 - Recursive Population Class In Programming...
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