Unit 1 Logical operators

Assessment Outcomes 4G Logical operations 4H Truth tables using up to 3 logical operations

Learning Intentions and Outcomes Learning Intention: To develop an understanding of the NOT, AND, OR, and XOR Logic gates Grade Pass Use AND, OR, NOT and XOR logical operators to create simple truth tables Grade Merit Combine logic gates to create logic circuits and filling in appropriate truth tables Analyse logic circuits to calculate an output, creating appropriate truth tables Grade Distinction Complete truth tables for standard logic circuits without the use of diagrams Combine 8 bit registers using standard logic operators

Starter Pre-Reading Recap What is a logic gate? What is the difference between a not gate and an or gate? What does an XOR gate do? What does an AND gate do? Describe how an OR gate works How many Inputs can a logic gate have? What happens when you combine an AND and a NOT gate? What is the difference between an AND and a NAND gate? If I have a 1 and a 0 pass through an AND gate what is the output? If I have a 1 and a 0 pass through a Not gate what is the output? If I have a 1 and a 0 pass through an OR gate what is the output?

Thinking Task What can you tell me about this?

Thinking Task What can you tell me about this? If there are CLOUDS and COLD there will be RAIN

Thinking Task What can you tell me about this? If A and B are TRUE then Q is TRUE

Thinking Task

Thinking Task Q=1 when A is not 1 Only 1 and 1 = 1 1 and 0 = 0 (or does not = 1)

Logical operators - Binary 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 four fundamental gates you know need to know about: NOT gate AND gate OR gate XOR gate (Exclusive 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 Logic Diagram

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 INPUT A B OUTPUT P Boolean Algebra: P = A AND B Logic Diagram

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 INPUT A B OUTPUT P Boolean Algebra: P = A OR B Logic Diagram

Boolean Algebra: P = A XOR B Binary Logic – XOR Gate If either input is 1 then the output is 1 UNLESS! Both are 1! Otherwise the output is 0 INPUT A B OUTPUT P Boolean Algebra: P = A XOR B Logic Diagram

Binary Logic – NAND Gate If both inputs are 1 then the output is 0 Otherwise the output is 1 It is the polar opposite of an AND gate! A B P 1 INPUT A B OUTPUT P Boolean Algebra: P = A AND B Truth Table Logic Diagram

Task Grade Pass Exercises Complete the Grade Pass Exercises Extension: The extension task asks you to combine multiple logic gates. Have a look at slides 16-18 to help you with this.

Combining Logic Gates We can string logic gates together to make more complex circuits Boolean Algebra: P = NOT (A AND B)

Combining Logic Gates We can string logic gates together to make more complex circuits Boolean Algebra: P = NOT (A AND B)

Combining Logic Gates We can string logic gates together to make more complex circuits Boolean Algebra: P = NOT (A AND B)

Combining Logic Gates WHAT GATE IS THIS? Boolean Algebra: P = NOT (A AND B)

Activity: Combined Logic Operators worksheet Draw a logic circuit of your own design that has at least 3 logic gates. You should also draw a truth table and write the Boolean algebra expression. 1

Graded Exercises Complete the Grade Merit and Distinction exercises You can use the pre-reading, PowerPoint, Internet to help you Grade Distinction* Extension: Check out the websites to learn a little more about how Logic Gates work Remember to be smart when using the Internet: Wikipedia is often complicated – sometimes even I don’t understand! BBC Bitesize, Teach ICT, and Revision World are better places to find your information!

Crib Sheet – What I must remember about ___ Starting Point: Read the learning outcomes from the exam board Record the key facts that you need to remember about Logical Operators! Think about what you have learnt today, what questions you have been asked, definitions of words, or anything else you think is important!

Homework Pre-Reading Notes: Low and High level programming languages Exercises: Complete the Merit level exercises