Lesson Objectives Aims You should be able to: Understand and produce simple logic diagrams Produce truth tables for NOT, AND and OR

Last lesson we learned computers are binary devices Recap Last lesson we learned computers are binary devices We know how binary works We understand binary can be represented with switches This is fundamental to the questions: Why do we use binary? How do we make something useful out of only switches?

Why binary? It just so happens switches (binary) are very cheap to produce Boolean Logic makes the creation of cheap, fast circuits possible These circuits are called “logic circuits” and are made up of combinations of the gates we will now look at

George Boole – man of amazing facial topiary Computers are all based on the principles of “Boolean Logic” Boolean was invented by George Boole in around 1849 – a time when computers didn’t exist. It is based on the idea of “truths” – things that will always follow a set of rules and always be correct

Computers use binary because: Binary can be represented by switches These switches can be combined to form “logic gates” – the basic building blocks of circuits We can base circuits on logic and prove, logically, that this works! We can have absolute reliability/proof our circuits will always do what we say they will Because of the nature of switches - circuits can only be in one of two states This results in more reliable circuits

January 2013 8(a)

Truth Tables Logical Truths are rules that apply to certain operators – AND, OR, NOT Each truth can be represented by a word and symbol Each operator has a set number of inputs and outputs

NOT The simplest logic gate Simply inverts the input Remember it by: “The output is NOT the input”

AND The AND gate is true ONLY if both inputs are true Useful for testing whether things are on or off (masking) Remember it by: “one AND the other input must be a 1”

OR The OR gate can be seen as (almost) representing binary addition (learn this next lesson) OR is true if any input is true Remember it by: “one OR the other must be true”

Circuits These simple gates can be combined to produce useful output or functionality Lets work through an exam question together to see how this might work

June 2014 – Q7

How do we tackle this question? A “truth table” must show the output for ALL possible combinations of inputs. So a circuit with 2 inputs A and B must have FOUR inputs. Put these in first

First step A B NOT (A AND B) 1

Next step Break the circuit down in to individual logic gates In this circuit we clearly AND together A and B, THEN we put the output of that through a NOT gate… So lets AND first…

Second Step A B A AND B NOT (A AND B) 1

Now we have the result of A AND B, we can do the second gate, which is a NOT. Simply take the output of A AND B and put it through a NOT gate…

Final Step A B A AND B NOT (A AND B) 1 Nice.

Jan 2013 Q3a

Jan 2013 Q3b

June 2012 Q3

June 2011 Q4

June 2011 Q4b

Work out the truth table for this circuit Homework/Extension Work out the truth table for this circuit A B D A OR B C A AND B E NOT (A AND B) S D AND E 1

Jun-14 Logic Gates and Truth Tables 7 Jan-13 3 May-12 May-11 4a