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Key Stage 3 lessons for the terrified BOOLEAN LOGIC TEACHER OVERVIEW Boolean Logic is a branch of Mathematics term commonly used in computing. It models how elements work together. Created by George Boole, an English mathematician, it is heavily used in the algebra of sets In most cases of Boolean Logic we consider a system that has one or two inputs. These inputs can be in one of two states, true or false. This is a binary system and has its equivalence in how computers work with electricity, to have power turned off or power turned on. These two states are normally associated with 0 and 1s. Another use of Boolean logic is when considering how searches are completed. However the latest versions of many search engines have negated the need to add logic terms to searches, although this is explored in the beginning of the lesson. It is quite an intellectual exercise to get learners to think about how electrical circuits can be used to process binary. How ‘dumb’ circuits can be created to add numbers together and the relation to how real computers work. There has to be careful progression to get to a meaningful end. Learners should have been taught about Binary numbers and how these can be added together before they tackle this lesson. Process: What do AND, OR and not mean? How do computer circuits process binary – the AND, OR and NOT gates? Creating a half adder circuit RESOURCES https://slp.somerset.gov.uk/cypd/elim/somersetict/Computing_curriculum_ks3_ks4/Forms/AllItems .aspx?RootFolder=%2fcypd%2felim%2fsomersetict%2fComputing%5fcurriculum%5fks3%5fks4%2fLo gic%20Gates&FolderCTID=&View=%7bE4E979BE%2d3409%2d4D54%2d8C10%2d8AC50A7F76E8%7d These include: Logic Presentation Logic Worksheet Large Logic Cards PowerPoint can be used throughout the lesson Worksheet for recording results A4 Cards with logic gates Key Stage 3 lessons for the terrified Load the PowerPoint presentation logic Show the second slide and ask them a question ‘Does a computer think?’ You should get some interesting answers and you should spend some time exploring these. Some can be quite philosophical and are worth taking the time to discuss quite widely. If you are really interested then do some research on the Turing Test –which is the accepted test to see if a machine exhibits intelligent behaviour. Now ask – if a machine can add two numbers is it intelligent? (Slide 3) How much human intervention does there have to be. State that we have learnt that every computer must use binary number and that they have previously learnt how to add binary numbers together. Maybe do a couple of sums to remind them how this was completed. Circuits within a computer are designed to work binary numbers in a logical fashion to complete tasks. Before we work with binary numbers let’s have a look at some logic statement and see if we can find out how these work. Show slide 4 and get them to complete the three different searches recording the number of sites that are found in the search. First search - One Second search – Direction Third Search – One Direction When we put in One AND Direction we got a better result. We used logic to complete the search. In fact, computers are inherently stupid – it is the way in which they are programmed that make them appear intelligent. Key Stage 3 lessons for the terrified This time get them to complete this search One Direction –Harry Styles and look at the number of results. What do we think the – does It is in fact a NOT and therefore should only display the pages about One Direction that have no reference to Harry Styles in them Computers are quite happy to work with this type of logic and there three basic logic gates that they use The – means Not and should mean that the websites displayed have no reference to Harry Styles They are called gates because the accept input which they then process and then allow these to be output AND, OR and NOT To further illustrate how these logic gates can work let us pretend that we are the manager of a nightclub. One of the issues is the ratio of females to males in the night club, we would like this to be as even as possible, and there are normally too many men. Unfortunately we have hired stupid bouncers and have to give them precise instructions to control the gender of the people that are allowed in. Select 3 bouncers for the class. Give each one a AND, OR or NOT card to represent a logic gate. Now select three pairs of learners: one pair should be both girls, the second a boy and a girl, the third both boys. Give the girls a card with a 1 and the boys a card with a zero. At the beginning of the evening the manager wants only girls to come so he uses his AND bouncer. Only if person one is female AND person two is female will he allow them to come in. Let the learners demonstrate this. Later on in the evening the ratio of male to female becomes better so the manager relaxes the rule a little and lets the OR bouncer take charge (The manager must not allow too many males in). Only if person one is female OR person two is female will he allow them in. Let the learners demonstrate this. The transistors on a semiconductor chip are constructed to allow electricity to run through them according to the inputs they receive. Some transistors act as AND gates, others as OR or NOT gates. There are in fact other types of gate called NAND and NOR which reverse the outputs from AND and OR gates. Chips can have over a billion transistors on them. Key Stage 3 lessons for the terrified There is one bouncer who has yet to do any work, the NOT bouncer. Now we have saved him to last as he only works with one person at a time, but what he does is special – he changes the sex of anyone who gets past him. Does anyone want to try? The presentations slides 7, 8 and 9 demonstrate this All computers use these three basic logic gates for all the work they complete. They help because the make decisions easy based on whether inputs are true or false, 0 or 1. Let’s run the slides again this time with 0 and 1 on the people Slides 10, 11 and 12 Now get them to fill in the truth tables on the worksheets we the correct numbers Slides 13 - 25 show the correct answers. The question is how we use the logic gates to add numbers together. Let’s consider the simplest job adding two binary digits together. We should get the answer shown on slide 26. Why does 1 + 1 = 10 and not 2 Slide 27 show a series of logic gates placed together in a circuit We are going to fill in Truth table as shown on the worksheet. He table looks like this Slide 28 Let’s trace the path thought the circuit. Slide 29. Put the number 0 and 0 into A and B of the first row. Click through the slide getting the learners to guess what is going to happen at each logic gate and filling in the columns as you go. The correct Truth Table is shown on slide 30 You can either then lead them thorough the next pair of number using slide 31 or let them have a go. This is true for all the next slides 31-36 Then show the last slide This part is difficult for many of the learners and according to their ability you should either lead them through this very slowly or let them complete some of the exercises