EBK ACTIVITIES MANUAL FOR PROGRAMMABLE
EBK ACTIVITIES MANUAL FOR PROGRAMMABLE
5th Edition
ISBN: 8220102795983
Author: Petruzella
Publisher: YUZU
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Chapter 11, Problem 7RQ
Program Plan Intro

Math instruction:

  • Math instructions refer to all output instructions that uses the data of two words or registers and perform the desired function.
  • Math instructions are program based on the type of processor used.
  • The data manipulation instructions are almost similar to math instructions.
  • The math instruction allows the PLC to take more of conventional computer qualities.
  • Math instructions are normally used to perform arithmetic functions on the values stored in memory words or registers.

Math functions:

The basic math functions performed by PLCs are as follows:

  • Addition
    • This function is used to add one piece of data to another.
    • It is also called as ADD.
  • Subtraction
    • This function is used to subtract one piece of data from another.
    • It is also called as SUB.
  • Multiplication
    • This function is used to multiply one piece of data by another.
    • It is also called as MUL.
  • Division
    • This function is used to divide one piece of data from another.
    • It is also called as DIV.

Terms used:

The following terms are used in the instruction.

  • Source A
    • Source A refers to the address of the first piece of data that is used in the instruction.
  • Source B:
    • Source B refers to the address of the second piece of data that is used in the instruction.
  • Destination
    • Destination refers to the address where the results of the instruction are stored.

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Suppose that the MinGap method below is added to the Treap class on Blackboard. public int MinGap ( ) Returns the absolute difference between the two closest numbers in the treap. For example, if the numbers are {2, 5, 7, 11, 12, 15, 20} then MinGap would returns 1, the absolute difference between 11 and 12. Requirements 1. Describe in a separate Design Document what additional data is needed and how that data is used to support an time complexity of O(1) for the MinGap method. Show as well that the methods Add and Remove can efficiently maintain this data as items are added and removed. (6 marks) 2. Re-implement the methods Add and Remove of the Treap class to maintain the augmented data in expected O(log n) time. (6 marks) 3. Implement the MinGap method. (4 marks) 4. Test your new method thoroughly. Include your test cases and results in a Test Document. (4 marks)
Suppose that the two Rank methods below are added to the Skip List class on Blackboard. public int Rank (T item) Returns the rank of the given item. public T Rank(int i) Returns the item with the given rank i. Requirements 1. Describe in a separate Design Document what additional data is needed and how that data is used to support an expected time complexity of O(log n) for each of the Rank methods. Show as well that the methods Insert and Remove can efficiently maintain this data as items are inserted and removed. (7 marks) 2. Re-implement the methods Insert and Remove of the Skip List class to maintain the augmented data in expected O(log n) time. Using the Contains method, ensure that added items are distinct. (6 marks) 3. Implement the two Rank methods. (8 marks) 4. Test your new methods thoroughly. Include your test cases and results in a Test Document. (4 marks)
Suppose that the two Rank methods below are added to the Skip List class on Blackboard. public int Rank (T item) Returns the rank of the given item. public T Rank(int i) Returns the item with the given rank i. Requirements 1. Describe in a separate Design Document what additional data is needed and how that data is used to support an expected time complexity of O(log n) for each of the Rank methods. Show as well that the methods Insert and Remove can efficiently maintain this data as items are inserted and removed. (7 marks) 2. Re-implement the methods Insert and Remove of the Skip List class to maintain the augmented data in expected O(log n) time. Using the Contains method, ensure that added items are distinct. (6 marks) 3. Implement the two Rank methods. (8 marks) 4. Test your new methods thoroughly. Include your test cases and results in a Test Document. (4 marks)
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