Introduction to Programming with C++, 3rd edition
3rd Edition
ISBN: 9780133377477
Author: Y. Daniel Liang
Publisher: Pearson Academic Computing
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Chapter 3, Problem 5PE
(Find future dates) Write a
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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 3 Solutions
Introduction to Programming with C++, 3rd edition
Ch. 3 - List six relational operators.
Ch. 3 - Prob. 2CPCh. 3 - Show the printout of the following code:
Ch. 3 - Write an if statement that assigns 1 to x if y is...Ch. 3 - Write an if statement that increases pay by 3 if...Ch. 3 - Prob. 6CPCh. 3 - Write an if statement that increases pay by if...Ch. 3 - Prob. 8CPCh. 3 - Prob. 9CPCh. 3 - Suppose Show the output, if any, of the following...
Ch. 3 - What is wrong in the following code?...Ch. 3 - Show the output of the following code:
Ch. 3 - Which of the following statements are equivalent?...Ch. 3 - Prob. 14CPCh. 3 - Are the following statements correct? Which one is...Ch. 3 - Prob. 16CPCh. 3 - Are the following statements equivalent?Ch. 3 - Prob. 18CPCh. 3 - a. How do you generate a random integer i such...Ch. 3 - Write an expression that obtains a random between...Ch. 3 - Prob. 21CPCh. 3 - (a) Write a Boolean expression that evaluates to...Ch. 3 - (a) Write a Boolean expression for x54.5. (b)...Ch. 3 - To test whether is between 10 and 100, which of...Ch. 3 - Are the following two expressions the same?
Ch. 3 - What is the value of the expression
Ch. 3 - Suppose, when you run the program, you enter the...Ch. 3 - Write a Boolean expression that evaluates to true...Ch. 3 - Write a Boolean expression that evaluates to true...Ch. 3 - Write a Boolean expression that evaluates to true...Ch. 3 - Write a Boolean expression that evaluates to true...Ch. 3 - What data types are required for a switch...Ch. 3 - What is y after the following switch statement is...Ch. 3 - What is x after the following if-else statement is...Ch. 3 - Suppose that, when you run the following program,...Ch. 3 - Rewrite the following if statements using the...Ch. 3 - Rewrite the following conditional expressions...Ch. 3 - List the precedence order of the Boolean...Ch. 3 - True or false? All the binary operators except =...Ch. 3 - Evaluate the following expressions:...Ch. 3 - ...Ch. 3 - (Algebra: solve quadratic equations) The two roots...Ch. 3 - (Check numbers) Write a program that prompts the...Ch. 3 - (Algebra: solve 22 linear equations) You can use...Ch. 3 - (Check temperature) Write a program that prompts...Ch. 3 - (Find future dates) Write a program that prompts...Ch. 3 - (Health application: BMI) Revise Listing 3.2,...Ch. 3 - Prob. 7PECh. 3 - (Financial application: monetary units) Modify...Ch. 3 - (Find the number of days in a month) Write a...Ch. 3 - (Game: addition quiz) Listing 3.4,...Ch. 3 - (Cost of shipping) A shipping company uses the...Ch. 3 - (Game: heads or tails) Write a program that lets...Ch. 3 - Prob. 13PECh. 3 - (Game: lottery) Revise Listing 3.7, Lottery.cpp,...Ch. 3 - (Game: scissor, rock, paper) Write a program that...Ch. 3 - (Compute the perimeter of a triangle) Write a...Ch. 3 - (Science: wind-chill temperature) Programming...Ch. 3 - (Game: addition for three numbers) Listing 3.4,...Ch. 3 - (Geometry: point in a circle?) Write a program...Ch. 3 - (Geometry: point in a rectangle?) Write a program...Ch. 3 - (Game: pick a card) Write a program that simulates...Ch. 3 - (Geometry: intersecting point) Two points on line...Ch. 3 - (Geometry: points in triangle'?) Suppose a right...Ch. 3 - (Use the operators) Write a program that prompts...Ch. 3 - (Geometry: two rectangles) Write a program that...Ch. 3 - (Geometry: two circles) Write a program that...Ch. 3 - Prob. 27PECh. 3 - (Financials: currency exchange) Write a program...Ch. 3 - Prob. 29PECh. 3 - (Financial: compare costs) Suppose you shop for...Ch. 3 - Prob. 31PECh. 3 - (Algebra: slope-intercept form) Write a program...Ch. 3 - (Science: day of the week)) Zeller's congruence is...Ch. 3 - Prob. 34PECh. 3 - (Business: check ISBN-10) An lSBN-10...Ch. 3 - (Palindrome number) Write a program that prompts...
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