GCSE OCR Computing A451 Binary logic 2-1-2 Computing hardware 6

Objectives 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

Why is binary so important? Reflected light Magnetic polarisation Power Trapped electrons

Why is binary so important? Fundamentally computers are electronic and can decide between two states – true or false, on or off, presence or absence of current and translate this into the binary representation of 1 or 0

Binary Logic As computers use transistors and capacitors to store binary data we can wire them together to make simple logical calculations These simple circuits are known as logic gates There are three fundamental gates you know need to know about: NOT gate AND gate OR gate

Boolean Algebra: P = NOT A Binary Logic – NOT gate If 0 is input it outputs 1 If 1 is input it outputs 0 INPUT A OUTPUT P Boolean Algebra: P = NOT A A P 1 Logic Diagram Truth Table

Boolean Algebra: P = A AND B Binary Logic – AND gate If both inputs are 1 then the output is 1 Otherwise the output is 0 A B P 1 INPUT A B OUTPUT P Boolean Algebra: P = A AND B Logic Diagram Truth Table

Boolean Algebra: P = A OR B Binary Logic – OR gate If either input is 1 then the output is 1 Otherwise the output is 0 A B P 1 INPUT A B OUTPUT P Boolean Algebra: P = A OR B Logic Diagram Truth Table

Order of Precedence Brackets NOT AND OR When combining logic gates, there are certain rules to follow to ensure you complete the circuits correctly. A bit like in maths where you need to use BIDMAS, with logic gates you need to know the Order of precedence It is: Brackets NOT AND OR

Combining logic gates We can string logic gates together to make more complex circuits INPUT A OUTPUT R P A B R = A AND B P = NOT R 1 Boolean Algebra: P = NOT (A AND B)

Combining logic gates We can string logic gates together to make more complex circuits OUTPUT R INPUT A OUTPUT P INPUT A A B R = A AND B P = NOT R 1 Boolean Algebra: P = NOT (A AND B)

Combining logic gates We can string logic gates together to make more complex circuits OUTPUT R INPUT A OUTPUT P INPUT A A B R = A AND B P = NOT R 1 Boolean Algebra: P = NOT (A AND B)

Increasing the number of inputs What happens if we had three inputs. How many possible combinations are there now? 32 = 2 x 2 x 2 = 8 possible input combinations OUTPUT P INPUT A B C R Boolean Algebra: P = (A AND B) OR C

Combining logic gates A B C R = A AND B P = R OR C Boolean Algebra: OUTPUT P INPUT A INPUT B INPUT C R Boolean Algebra: P = (A AND B) OR C

Combining logic gates A B C R = A AND B P = R OR C 1 Boolean Algebra: 1 OUTPUT P INPUT A INPUT B INPUT C R Boolean Algebra: P = (A AND B) OR C

Practise makes perfect In the exam you will need to be able to do the following: Complete truth tables from a logic diagram Produce simple logic diagrams from Boolean algebra An excellent site to practise is: http://logic.ly