1. Activity 1 Revise / remember what the term ‘binary logic’ means. What do each of the following look like: NOT gate? AND gate? OR gate? 5 minutes

2. Binary Logic Circuits How do the gates work together to process data?

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 it will really hurt my finger'. …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? Using rules we can work out the truth of the following: 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 takes 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 takes 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 a sensible outputs, based on these rules (inputs) True (using an AND gate)

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. Worked Examples AQ AQ 10 0 1

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

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

12. Binary Logic Circuits In your exam you will be expected to be able to look at a circuit and produce a truth table for the inputs and outputs. 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 A B Q ABQ ?

13. Binary Logic Circuits Worked Example 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 A B P Q INPUTS: A, B, C etc OUTPUTS: P, Q, R etc A B Q = A AND BP = NOT (A AND B) 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 P = NOT Q

14. Binary Logic Circuits Worked Example 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 A B P Q INPUTS: A, B, C etc OUTPUTS: P, Q, R etc A B Q = Not AP = (NOT A) AND B 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 P = Q AND B

15. Binary Logic Circuits Worked Example 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 A B P ABCQ = A AND BP = (A AND B) OR C Q INPUTS: A, B, C etc OUTPUTS: P, Q, R etc C 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0

16. Binary Logic Circuits Tips: 1.Label the inputs on the circuit diagram 2.Label the outputs on the circuit diagram 3.Create a table with a column for each input and output 4.Label the columns (outputs labelled in the form of an expression) 5.Place the combinations of different zeros and ones in the input columns 6.Workout the outputs for each output column in turn 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 A B P Q INPUTS: A, B, C etc OUTPUTS: P, Q, R etc A B Q = A AND BP = NOT (A AND B) 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1

17. Binary Logic Circuits Tips: 1.When you place the combinations of different zeros and ones in the input columns…there are patterns that you can remember to help you… 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 A B 1 1 0 0 1 0 1 0 ABC 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 What if there were 4 inputs? 2 inputs 3 inputs