# Classical and Quantum Computing: with C++ and Java Simulations # Classical and Quantum Computing: with C++ and Java Simulations

## Yorick Hardy

Language: English

Pages: 589

ISBN: 3764366109

Format: PDF / Kindle (mobi) / ePub

This is a self-contained, systematic and comprehensive introduction to all the subjects and techniques important in scientific computing. The style and presentation are readily accessible to undergraduates and graduates. A large number of examples, accompanied by complete C++ and Java code wherever possible, cover every topic.

QM3 ,1 = 0 Thus we have reduced the expression to one consisting of only two types of operations and 5 operations in total. This is a large reduction compared to the original total of 11 operations. The example also illustrates that the process is long but simple .. enough to implement, making it a good application for a computing device. 2.7 Example Programs 41 2.7 Example Programs 2.7.1 Efficient Set Operations Using Boolean Algebra Let U := { 00,01, ... ,On-1 } be the universal set of n

19 3.37 x 10-4932 < Data Type Approximate Normalized Range (Decimal) X S; +2 X X 109 S; +9 x 1018 Ixl < 3.40 x 1038 Ixl < 1.79 x 10308 Ixl < 1.18 x 104932 All operands are stored in memory with the least significant digits starting at the initial (lowest) memory address. Numeric instructions access and store memory operands using only this initial address. 74 Chapter 3. Number Representation 3.2.2 Representation The first step to understanding how a binary fraction is stored using

for creating and destroying a list, copying one list to another (assignment operator), adding items to and removing items from the list (additem, insert item, removeitem), merging lists (operators for addition), iteration (first, next, last, position, data) and indexing elements (operator[]). 9.2 Linked List II list.h #ifndef LIST_HEADER #define LIST_HEADER using namespace std; template struct listitem { T data; list item *next; }; template class list { protected:

3) a' = 4 and b' = 3 • 2) q = 1 and r = 1 • 3) a' = 3 and b' = 1 • 2) q = 3 and r = 0 • 4) The GCD is 1. 1.1 Algorithms 5 Definition. Execution of an algorithm refers to the following (or execution) of the steps given in the algorithm. Definition. Termination of an algorithm is when an algorithm finishes, there is nothing more to be done. An algorithm executes uniquely if, for a given input, the termination of the algorithm is always the same, i.e. the variables, memory, state, output and

5.9 Binary 5.8.1 5.8.2 5.8.3 Binary Multiplication . . . . . Unsigned Integer Multiplication Fast Multiplication . . . . . . Signed Integer Multiplication Division . . . . . . . . . . . . 91 92 93 96 97 98 98 99 .100 · 101 · 102 · 103 · 103 · 105 · 106 · 107 Contents vii 5.10 Magnitude Comparator . . . .108 5.11 4-Bit ALU .......... · 110 5.12 Read Only Memory (ROM) . · 112 5.13 Combinational Programmable Logic Devices · 113 5.14 Programmable Gate Arrays . · 117 5.15