GCSE Computing – Topic 2 Lesson 5a – Binary Logic CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram.

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Starter Everyone stand up, if you meet the criteria sit down. Consider the choice of words I am using, how does this word affect whether you stand up or sit down? AND – OR – NOT -

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Binary Logic We already know that Binary is used by represent data in a computer system. It uses a 1 or a 0 to represent data. As computers use electrical circuits they have two states ON or OFF (1 or 0). Logic gates use binary logic to take inputs as a 1 or 0 and given an output of 1 or 0. Binary logic is where we say if something is either true or false. There is no maybes or kind of. Just true or false. For example “Is that a car?” would result in true or false (It is either a car or it isn’t). Or “Mr Stead has a beard today”. Statements like “Is Mr Stead awesome?” would NOT be binary logic as the answer will not be answered the same by different people.

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Types of Logic Gates Stick the sheet you have been given in your book, for each type of logic gate, based on the input of A, B or both, decide whether the output is 1 or 0. Remember: AND – All has to be TRUE (1) for the output to be TRUE (1) OR – At least 1 has to be TRUE (1) for the output to be TRUE (1) NOT – the output is the opposite of the input.

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. NOT – Logic Gate NOT– reverses truth. True becomes false and false becomes true! Key point – This flips truth! AB 0 1 A B

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. AND – Logic Gate AND – If A and B are both true then C is true. Key point – Both MUST be true for AND to be true! ABC A B C

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. OR – Logic Gate OR– If either A or B are true then C is true Key point – At least one of A or B must be true! ABC A B C

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Quick Test – Binary Logic For each question, look at the logic diagram and decide what the output for each would be. A)1 0 ? B) 0 ? C) 0 1 ? D) 1 ? E) 0 1 ?

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Logic Circuits Logic Gates can be combined into logic circuits, and the output from one logic gate can feed another. A logic gate that follows another logic gate, uses the output from it to feed it’s input, all possible outcomes must be considered. Rule of thumb: The number of rows in the truth table can be calculated by: 2 n where n = Number of Inputs 2 inputs (A,B) = 4 rows 3 inputs (A,B,C) = 8 rows etc.

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Logic Circuits Working out the output using logic circuits 1.Calculate the number of rows in the truth table by identifying the inputs. 2.Work out the binary combinations using those inputs. e.g. 3 inputs would be all the binary combinations to represent 0 to 7 using 3 bits. 000, 001, 010, 011, 100, 101, 110, Start at the beginning of the logic circuit and calculate the output. 4.Repeat for the next logic gate.

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Worked Example Complete the truth table for the following logic circuit. A B C D ABCD

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Group Task You will work in groups to complete the truth tables for a range of different scenarios, they start off easy and get harder. Start at difficulty level 1, you must try to complete one task from each difficulty level. As you have completed a level, come get it checked and then pick one from the next level. If you are confident in your ability, start at Level 2.

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Exercise - Extension Draw the following diagrams in your book and complete a truth table for each task: a)c) b)d) A B C D A B C D E A BC D A B C D E F

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Progress Check / Plenary Using your mini-whiteboards, lets check our progress against the outcomes: A B C Name the Logic Gate

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Progress Check / Plenary Using your mini-whiteboards, lets check our progress against the outcomes: Name the Logic Gate A B C

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Progress Check / Plenary Using your mini-whiteboards, lets check our progress against the outcomes: Name the Logic Gate A B

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Progress Check / Plenary Using your mini-whiteboards, lets check our progress against the outcomes: Draw the Truth Table A B C D E

CHALLENGE TO: identify the different types of logic diagrams. ASPIRE TO: Construct a truth table for a given logic diagram. Progress Check / Plenary Using your mini-whiteboards, lets check our progress against the outcomes: How many inputs? How many rows in the truth table? A B C D E F

GCSE Computing – Topic 2 Lesson 5b – Binary Logic CHALLENGE TO: Construct a logic circuit for a given statement with 2 inputs ASPIRE TO: Construct a logic circuit for a given statement with more than 2 inputs

CHALLENGE TO: Construct a logic circuit for a given statement with 2 inputs. ASPIRE TO: Construct a logic circuit for a given statement with more than 2 inputs Logic Gates So far we have been given logic gates/circuits and constructed truth tables for them, however you could also be asked to create a logic gate/circuit based on a statement. e.g. Draw a logic circuit for A AND NOT(B OR C) This example would look something like above, so how do you get to this? A B C

CHALLENGE TO: Construct a logic circuit for a given statement with 2 inputs. ASPIRE TO: Construct a logic circuit for a given statement with more than 2 inputs Logic Gates First of all you have to make sure you know what each logic gate looks like when written. A NOT A A B A AND B A OR B A B

CHALLENGE TO: Construct a logic circuit for a given statement with 2 inputs. ASPIRE TO: Construct a logic circuit for a given statement with more than 2 inputs Worked Example - Logic Circuits You must then break down the expression and create each logic gate required separately, before combining them. It is normally a good idea to construct the gate in brackets first, just like you would do a calculation in the brackets first. e.g. (A OR B) AND NOT(C) A B A OR B C NOT C COMBINED A B C

CHALLENGE TO: Construct a logic circuit for a given statement with 2 inputs. ASPIRE TO: Construct a logic circuit for a given statement with more than 2 inputs Task Create the logic circuits for the following expressions, make sure you write the expression first: a)(NOT B) AND A b)(A AND B) OR (C AND D) c)A OR (B AND C) or D d)(A AND B) AND (C AND D) e)(NOT A) OR (NOT B) AND C Swap books with the person next to you and peer assess their work, remember to initial it.

CHALLENGE TO: Construct a logic circuit for a given statement with 2 inputs. ASPIRE TO: Construct a logic circuit for a given statement with more than 2 inputs Consolidating Using everything you have learn today, complete the worksheet on logic gates: