Starting Out with C++ from Control Structures to Objects (9th Edition)
9th Edition
ISBN: 9780134498379
Author: Tony Gaddis
Publisher: PEARSON
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Textbook Question
Chapter 20, Problem 12PC
Ackermann’s Function
Ackermann’s Function is a recursive mathematical
If m = 0 then return n + 1
If n = 0 then return A(m−1, 1)
Otherwise, return A(m−1, A(m, n−1))
Test your function in a driver
A(0, 0) A(0, 1) A(1, 1) A(1, 2) A(1, 3) A(2, 2) A(3, 2)
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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 20 Solutions
Starting Out with C++ from Control Structures to Objects (9th Edition)
Ch. 20.2 - What happens if a recursive function never...Ch. 20.2 - What is a recursive functions base case?Ch. 20.2 - Prob. 20.3CPCh. 20.2 - What is the difference between direct and indirect...Ch. 20 - What is the base case of each of the recursive...Ch. 20 - What type of recursive function do you think would...Ch. 20 - Which repetition approach is less efficient, a...Ch. 20 - When should you choose a recursive algorithm over...Ch. 20 - Explain what is likely to happen when a recursive...Ch. 20 - The _____________ of recursion is the number of...
Ch. 20 - Prob. 7RQECh. 20 - Prob. 8RQECh. 20 - Prob. 9RQECh. 20 - Write a recursive function to return the number of...Ch. 20 - Write a recursive function to return the largest...Ch. 20 - #include iostream using namespace std; int...Ch. 20 - Prob. 13RQECh. 20 - #include iostream #include string using namespace...Ch. 20 - Iterative Factorial Write an iterative version...Ch. 20 - Prob. 2PCCh. 20 - Prob. 3PCCh. 20 - Recursive Array Sum Write a function that accepts...Ch. 20 - Prob. 5PCCh. 20 - Prob. 6PCCh. 20 - Prob. 7PCCh. 20 - Prob. 8PCCh. 20 - Prob. 9PCCh. 20 - Prob. 10PCCh. 20 - Prob. 11PCCh. 20 - Ackermanns Function Ackermanns Function is a...
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