1. Think about the following expression If the number entered is greater than 15 but less than 25 or the number is 100 and the letter chosen is after p but less than Z and not the letter T or his name entered is greater than 4 characters and not “Steve” then say “Excellent” else say “Bogus!” What would be the results for 1)11, Q, “Roger” 2)100,T,”Bob” 3)20,A,”Steve”

2. © GCSE Computing Candidates should be able to:  explain why data is represented in computer systems in binary form  understand and produce simple logic diagrams using the operations NOT, AND and OR  produce a truth table from a given logic diagram. Slide 2

3. © GCSE Computing  The denary (decimal) system that we use has 10 digits (0-9).  For a computer systems to use denary it would need to be able to store and transmit 10 different ‘states’.  It is therefore much simpler for computer systems to use the binary number system because it has just 2 digits (0-1) which can easily be represented and stored as 2 different states.  Examples of different ‘states’ used to store/transmit binary data:  ON / OFF (a semi-conductor switch, used in computer memory)  TRANSMIT / DON’T TRANSMIT (an electrical signal, used to transfer binary data)  NORTH / SOUTH (areas with different magnetic polarity, used to store binary data on magnetic media)  REFLECT / NON-REFLECT (reflective and non-reflective areas, used to store binary data on optical media) Slide 3

4. © GCSE Computing  In computer science, the Boolean or logical data type is a data type that has two values (usually denoted true and false).  Logic gates are physical devices that can carry out Boolean logic functions.  The three basic logic gates are the AND, OR and NOT gates. Slide 4

5. © GCSE Computing  The symbol for an AND gate is shown below.  OUTPUT O is only true if INPUT A AND INPUT B are both TRUE.  This can be represented by this truth table.  It can also be represented by this logic statement: O = A AND B  An AND gate carries out Boolean multiplication (i.e. TRUE * FALSE = TRUE) Slide 5 INPUTOUTPUT 000 010 100 111

6. © GCSE Computing  The symbol for an OR gate is shown below.  OUTPUT O is true if INPUT A OR INPUT B are TRUE.  This can be represented by this truth table.  It can also be represented by this logic statement: O = A OR B  An OR gate carries out Boolean addition (i.e. TRUE + TRUE = TRUE) Slide 6 INPUTOUTPUT 000 011 101 111

7. © GCSE Computing  The symbol for a NOT gate is shown below.  OUTPUT O is true if INPUT A is NOT TRUE.  This can be represented by this truth table.  It can also be represented by this logic statement: O = NOT A  A NOT gate carries out Boolean inversion (i.e. TRUE = FALSE) Slide 7 INPUTOUTPUT 01 10

8. © GCSE Computing Slide 8  A logic diagram is a diagram that represents one or more of logic gates linked together to form a logic circuit.  In logic diagrams;  Symbols are used to represent logic gates  Letters are used to label the input(s) and output(s)  Lines are used to show how logic gates are connected.

9. © GCSE Computing Slide 9 In this logic diagram, the output will be FALSE only when inputs A and B are both TRUE. This logic diagram can be written as a logic statement: O = NOT (A AND B) In this logic diagram, the output will be TRUE only when inputs A and B are both FALSE. This logic diagram can be written as a logic statement: O = NOT (A OR B) In this logic diagram, the output will be TRUE only when input A is FALSE and input B is TRUE. This logic diagram can be written as a logic statement: O = (NOT A) AND B

10. © GCSE Computing INPUTOUTPUT ABO 001 011 101 110 Slide 10 INPUTOUTPUT ABO 001 010 100 110 INPUTOUTPUT ABO 001 010 100 110

11. © GCSE Computing Slide 11  For each logic diagram, complete a truth table and create a logic statement.

12. © GCSE Computing Slide 12  For each logic statement, complete a truth table and create a logic diagram.  O = (NOT A) AND (NOT B)  O = NOT (A OR (NOT B))

13. © GCSE Computing Slide 13  For each truth table, create a logic diagram and create a logic statement. INPUTOUTPUT ABO 000 011 101 110 INPUTOUTPUT ABO 000 010 101 110