1. Unit 18: Computational Thinking
Pre-enrolment

2. Unit introduction Computers influence much of the world around us
used to solve a range of problems,
generating the visual effects in films
landing the Curiosity Rover (unmanned robot) on Mars.
use mathematics and logic.

3. Numbers – an invention
No problem,
I have food, clothing

4. More than one…
Still not a problem,
just give them names

5. Lots more than one
Now need a system

6. Egyptians

7. Decimal system Introduces a zero Invented by independently by:
Babylonians,
Mayans
Indians
Uses place value
The value of a symbol depends on where it appears in the number: eg 33
333
3333 etc

8. Decimal system
10 symbols
0 – 9
Click over to new place value after 9

9. Other systems Binary Hexadecimal Base 2 Uses 1 & 0 Base 16
Uses additional symbols (A,B,C,D,E,F)

10. Binary Basis of electrical data transmission Decimal Binary
0 = no current flowing
1 = current flowing
Decimal
Binary

11. Task
7, 5, 102
11, 1011,

12. three types of computational thinking skills
Logical thinking
Algorithmic thinking
Optimal thinking

13. Logical thinking
Work out how logical thinking is applied to the following games/puzzles:
Sudoku
Minesweeper

14. Sudoku What are the ‘rules’?
Using the rules, what is this number? (There is only one possibility).

15. Minesweeper
The numbers indicate how many of the 8 surrounding squares have ‘mines’.
There are 10 mines here, how many can you
place from this start?

16. Finished game
4 of the mines
could be placed
From the
original screen.

17. Logical thinking Don’t need to know Just use the available information
number bonds
Multiplication tables
Complex maths
Just use the available information
Don’t guess!

18. Algorithmic thinking A bit like logical thinking
uses a predefined set of instructions to solve problems
E.g.
strategy games
Chess

19. Algorithmic thinking Don’t need to know Just follow the instructions
number bonds
Multiplication tables
Complex maths
Just follow the instructions

20. Optimal thinking
refining one of many possible solutions to a problem to make it more efficient
E.g.
Rubik’s Cube
Towers of Hanoi

21. Towers of Hanoi http://www.mathsisfun.com/games/towerofhanoi.html
Give it a go – what is your best score?
What if there were 4 pegs?
Best score is 7
The minimum number of moves required to solve a Tower of Hanoi puzzle is 2n - 1, where n is the number of disks
Frame–Stewart algorithm[edit]
The Frame–Stewart algorithm, giving a presumably optimal solution for four (or even more) pegs, is described below:
Let  be the number of disks.
Let  be the number of pegs.
Define  to be the minimum number of moves required to transfer n disks using r pegs
The algorithm can be described recursively:
For some , , transfer the top  disks to a single peg other than the start or destination pegs, taking  moves.
Without disturbing the peg that now contains the top  disks, transfer the remaining  disks to the destination peg, using only the remaining  pegs, taking  moves.
Finally, transfer the top  disks to the destination peg, taking  moves.
The entire process takes  moves. Therefore, the count  should be picked for which this quantity is minimum.
This algorithm (with the above choice for ) is presumed to be optimal, and no counterexamples are known.

22. Boolean Algebra
What does this mean?

23. Boolean logic
Boolean algebra deals with the values 0 and 1 or the values false and true ‘the algebra of truth’
It is ideally suited for use in a computer: WHY?
Operations using just 0 and 1 can be easily replicated using simple electronic circuits
AND OR
NOT
XOR

24. Truth Tables Boolean Operations are represented in Truth tables
Input (s)
Input A
Input B
Output
The operations are carried out by electronic ‘gates’
INPUT
OUTPUT

25. The simplest function - NOT
The NOT gate takes an input and reverses it.  also known as an inverter
If the input is 1, the output is 0
If the input is 0, the output is 1
(very useful for 2s complement when we flip the bits)
INPUT
OUTPUT A
NOT A 1
Symbol (used on circuit diagrams)
Truth table

26. Task Find symbols and meanings for: AND OR NOT XOR
Can you also write a truth table for each?

27. AND A 1 is required on both inputs to give a 1 at the output
Only returns a high value if both inputs are high.
INPUT
OUTPUT A B
A AND B 1
Symbol
Truth table

28. OR A 1 on either input gives a 1 at the output.
Gives a high output if at least one of the inputs is high
INPUT
OUTPUT A B
A OR B 1
Symbol
Truth table

29. Exclusive OR (EXOR XOR)
You only get a 1 at the output when the two inputs are different
Returns a high output if either (but not both) of the inputs is high.
INPUT
OUTPUT A B
A XOR B 1
Symbol
Truth table

30. Other gates There are other gates:

31. How do Boolean operations help?
Searches:
Help to refine searches:
Find ‘this term’ AND ‘this term’
Find either ‘this term’ or ‘this term’ (or both)
Find ‘this term’ but not ‘this term’
Etc

32. Programming Can be used with conditional statements:
E.g. ‘if’ statements

33. Addition So how can we use logic gates to add up?
Need to know the rules of binary arithmetic:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 and carry 1

34. Your task Complete the task before leaving today and email to: