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Published byPoppy Craig Modified over 9 years ago
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Teaching Computing to GCSE Level with Python Session 3
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Your second starter! 1. Convert these binary numbers to denary: 0 1 0 1 0 0 1 01 0 1 1 0 1 1 0 2. Convert the same numbers to hex 3. Convert these hex numbers to binary A 34 F2 42 9 4. Convert these binary numbers to hex 0 1 1 1 0 0 0 11 0 1 1 0 1 0 1 5. What is the largest denary number you can express in 9 bits? 6. How many different values can you show using 9 bits?
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Topics for today Theory Binary logic: AND, OR, NOT Truth tables Logic Gates www.logic.ly www.logic.ly Programming IF Statements
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Binary logic GCSE Computing link to specification Recap on binary numbers AND OR NOT Truth tables Logic diagrams Logic.ly
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Link to specification (OCR GCSE Computing Specification) Candidates should be able to: (d) explain why data is represented in computer systems in binary form (e) understand and produce simple logic diagrams using the operations NOT, AND and OR (f) produce a truth table from a given logic diagram. (a, b and c are points that relate to the CPU)
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AND OR NOT For A AND B to be true, then A must be true and B must be true For example, “It is true that Cambridge United won last week and there was 5 cm of snow on Friday” is only true if both are true. For A OR B to be true then at least one of A and B must be true “It is true that Cambridge United won last week OR there was 5 cm of snow on Friday” is true if only one of the individual statements is true NOT A is always the opposite of A. So if A is true, NOT A is false. For example, “It is not raining” is true if “It is raining” is false
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The NOT gate (inverter) Note there is 1 input, A, and 1 output (often called Q) We can also represent this mathematically as Diagrammatic representation of a NOT gate A the bar notation represents logical NOT A
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The AND gate Note there are 2 inputs, A and B, and 1 output Q We can also represent this mathematically as A. B (the dot notation represents logical AND) Diagrammatic representation of an AND gate
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The OR gate Note there are 2 inputs, A and B, and 1 output Q We can also represent this mathematically as A + B (the + notation represents logical OR) Diagrammatic representation of an OR gate
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Truth Tables A truth table shows the output values for all the different input combinations.
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Task Complete the truth tables on the sheet As a minimum, do AND, NOT and OR Extension – try the remaining ones
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Using Logic.Ly Go to http://logic.ly/ and select Try Onlinehttp://logic.ly/ Close the demo box offered Drag the gates and inputs and outputs to the main window Try to build and AND, NOT and an OR circuit
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Try these circuits: Circuit 1
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Circuit 1 0 1 1 1 1 0 0 0
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Circuit 2
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0 0 0 1 1 1 1 0
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Circuit 3
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0 1 1 1 1 0 1 0 0 0 1 0
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Circuit 4 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1
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Circuit 5 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0
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Circuit 6 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0
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