Starting Out with Python Plus MyLab Programming with Pearson eText -- Access Card Package (4th Edition)
4th Edition
ISBN: 9780134543666
Author: Tony Gaddis
Publisher: PEARSON
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Question
Chapter 12.2, Problem 2CP
Program Plan Intro
Problem Solving:
In Python, a problem can be divided into smaller parts only if it has an identical structure to the whole problem. Then, it can be solved using recursion.
Working method of recursive function:
A recursive function has two approaches. They are as follows:
- • If a problem can be solved currently without using recursion, then use function to solve it and returns.
- • If a problem cannot be solved currently, then the function reduces the problem into smaller parts only if it has a similar structure to the whole
program . And the function calls itself to solve the sub-parts.
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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 12 Solutions
Starting Out with Python Plus MyLab Programming with Pearson eText -- Access Card Package (4th Edition)
Ch. 12.2 - It is said that a recursive algorithm has more...Ch. 12.2 - Prob. 2CPCh. 12.2 - What is a recursive case?Ch. 12.2 - What causes a recursive algorithm to stop calling...Ch. 12.2 - What is direct recursion? What is indirect...Ch. 12 - Prob. 1MCCh. 12 - A function is called once from a program's main...Ch. 12 - Prob. 3MCCh. 12 - Prob. 4MCCh. 12 - Prob. 5MC
Ch. 12 - Prob. 6MCCh. 12 - Any problem that can be solved recursively can...Ch. 12 - Actions taken by the computer when a function is...Ch. 12 - A recursive algorithm must _______ in the...Ch. 12 - A recursive algorithm must ______ in the base...Ch. 12 - An algorithm that uses a loop will usually run...Ch. 12 - Some problems can be solved through recursion...Ch. 12 - It is not necessary to have a base case in all...Ch. 12 - In the base case, a recursive method calls itself...Ch. 12 - In Program 12-2 , presented earlier in this...Ch. 12 - In this chapter, the rules given for calculating...Ch. 12 - Is recursion ever required to solve a problem?...Ch. 12 - When recursion is used to solve a problem, why...Ch. 12 - How is a problem usually reduced with a recursive...Ch. 12 - What will the following program display? def...Ch. 12 - Prob. 2AWCh. 12 - The following function uses a loop. Rewrite it as...Ch. 12 - Prob. 1PECh. 12 - Prob. 2PECh. 12 - Prob. 3PECh. 12 - Largest List Item Design a function that accepts a...Ch. 12 - Recursive List Sum Design a function that accepts...Ch. 12 - Prob. 6PECh. 12 - Prob. 7PECh. 12 - Ackermann's Function Ackermann's Function is a...
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