1. Activity 1 Revise/research what the word binary means Revise/research what the word logic means 5 minutes

2. Binary Logic What is Logic ? What is Binary Logic ?

3. Introduction to Binary Logic What is Logic? In general, we use 'logic' to work out whether doing something causes the result to be 'True' or 'False'. Consider the painful experiment below: 'If I stick my finger in boiling water then I will make my finger really hurt!'. …Is this a True statement? Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram

4. Introduction to Binary Logic What is Logic? We can use some rules to work out the truth of this: Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram Rule 1 : I am human Rule 2 : Boiling water burns human skin My finger will burn if I dip it in boiling water We think using logic. With logic we take inputs (known rules) and produce a sensible output, based on these rules (inputs) True

5. Introduction to Binary Logic What is Logic? Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram Rule 2 : I’m a cat Rule 1 : Cats cough up fur balls. I will therefore cough up fur balls We think using logic. With logic we take inputs (known rules) and produce a sensible output, based on these rules (inputs) False True False

6. Introduction to Binary Logic What is Logic? Human logic works with rules / facts / statements which are either True or False : Cats cough up fur balls: TRUE I am a cat: FALSE So Logically… I will cough up fur balls FALSE The earliest computer scientists quickly understood that logic can be used within a computer to work out problems. Remember…computer data is either 1 (Logic True) or 0 (Logic False). Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram Inputs Output

7. Introduction to Binary Logic What is Binary Logic? Binary logic, put simply, is how the CPU makes decisions based on the inputs it gets. The CPU (like us) will take inputs which may be true or false (1 or 0) and make a decision which will produce a particular output. Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram Input 2: 1 Input 1: 1 Logically, the output will be 1 Computers think using binary logic. With binary logic computers take inputs (zeros and ones) and produce sensible outputs, based on these rules (inputs) True

8. Introduction to Binary Logic What is Binary Logic? There are only a few simple logic operations that a CPU will perform on its inputs, but combinations of these lead to incredibly complex calculations. The logic operations that a CPU will perform are: a) The NOT operation b) The AND operation c) The OR operation Electronics engineers created hardware that can carry out the AND, OR and NOT logic operations and it is these pieces of hardware that makes up the CPU. Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram

9. Introduction to Binary Logic What is Binary Logic? This hardware is known as a 'logic gate'. A logic gate is created from a number of transistor switches arranged in particular ways. They are too small to see so we use symbols to represent what the 3 different types of logic gates are Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram

10. Introduction to Binary Logic Invert or NOT operation This operation produces an output that is opposite to the input. If the input is 1 (Logic True) then the output is 0 (Logic False). If the input is 0 (Logic False) then the output is 1 (Logic True) The shorthand way of writing this is Q = NOT A where 'A' is the input and 'Q' is the output. It does not have to be A and Q, you could use any letter, but Q is a popular choice to describe a logic output. Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram 1 0 0 1

11. Introduction to Binary Logic The AND operation This operation acts upon at least two inputs, say A, B to produce a single output Q. In English, the rule is: "If both A and B are True then the output is also True, otherwise it is False”. The shorthand for this is Q = A AND B Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram 1 1 1 0 1 0 0 0 1 0 0 0

12. Introduction to Binary Logic The OR operation Again, this needs at least two inputs A, B to produce a single output. In English the rule is: "If either or both A, B are True then the output is also True”. The shorthand for this is Q = A OR B Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram 1 1 1 0 1 1 1 1 0 0 0 0

13. Introduction to Binary Logic Truth Tables Truth tables are used to record / write down all of the inputs that a logic gate can have… and …the outputs that are produced from its operation. Learning Objectives: (a)Explain why data is represented in computer systems in binary form (b)Understand and produce simple logic diagrams using the operations NOT, AND and OR (c)Produce a truth table from a given logic diagram

14. Worked Examples AQ AQ 10 0 1

15. A Q ABQ B 11 1 1 0 0 010 000

16. A Q ABQ B 111 1 01 0 11 0 0 0

17. Activity 2 Create a presentation which clearly explains the following: 1.What binary logic is 2.What the three logic gates are (and what they do) 3.What truth tables are and how they work for each gate 15 minutes