Data Structures and Algorithms in Java
6th Edition
ISBN: 9781119278023
Author: Michael T. Goodrich; Roberto Tamassia; Michael H. Goldwasser
Publisher: Wiley Global Education US
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Textbook Question
Chapter 1, Problem 19C
Write a Java
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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 1 Solutions
Data Structures and Algorithms in Java
Ch. 1 - Prob. 1RCh. 1 - Suppose that we create an array A of GameEntry...Ch. 1 - Write a short Java method, isMultiple, that takes...Ch. 1 - Write a short Java method, isEven, that takes an...Ch. 1 - Write a short Java method that takes an integer n...Ch. 1 - Write a short Java method that takes an integer n...Ch. 1 - Write a short Java method that takes an integer n...Ch. 1 - Write a short Java method that counts the number...Ch. 1 - Prob. 9RCh. 1 - Prob. 10R
Ch. 1 - Modify the CreditCard class from Code Fragment 1.5...Ch. 1 - Prob. 12RCh. 1 - Modify the declaration of the first for loop in...Ch. 1 - Prob. 14CCh. 1 - Write a pseudocode description of a method for...Ch. 1 - Write a short program that takes as input three...Ch. 1 - Write a short Java method that takes an array of...Ch. 1 - Prob. 18CCh. 1 - Write a Java program that can take a positive...Ch. 1 - Write a Java method that takes an array of float...Ch. 1 - Write a Java method that takes an array containing...Ch. 1 - Prob. 22CCh. 1 - Write a short Java program that takes two arrays a...Ch. 1 - Modify the CreditCard class from Code Fragment 1.5...Ch. 1 - Modify the CreditCard class to add a toString()...Ch. 1 - Write a short Java program that takes all the...Ch. 1 - Write a Java program that can simulate a simple...Ch. 1 - A common punishment for school children is to...Ch. 1 - The birthday paradox says that the probability...Ch. 1 - (For those who know Java graphical user interface...
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