Activity 1 5 minutes Grab a whiteboard and pen, come to the front and work out the Truth Table for the following circuit: R A B C Q

How do the gates work together to process data? Binary Logic Circuits How do the gates work together to process data?

? Binary Logic Circuits Remembering Last Lesson Binary Logic Circuits Learning Objectives: why data is represented in computer systems in binary form simple logic diagrams using the operations AND, OR and NOT truth tables combining Boolean operators using AND, OR and NOT to two levels. applying logical operators in appropriate truth tables to solve problems applying computing-related mathematics: +, -, /, *, Exponentiation (^), MOD, DIV Remembering Last Lesson Binary Logic Circuits In your exam you will be expected to be able to look at a circuit and produce a truth table for the inputs and outputs. A B Q ? A B Q

Binary Logic Circuits Worked Example Q A P B A B Q = Not A Learning Objectives: why data is represented in computer systems in binary form simple logic diagrams using the operations AND, OR and NOT truth tables combining Boolean operators using AND, OR and NOT to two levels. applying logical operators in appropriate truth tables to solve problems applying computing-related mathematics: +, -, /, *, Exponentiation (^), MOD, DIV Worked Example Q A P B A B Q = Not A P = (NOT A) AND B P = Q AND B INPUTS: A, B, C etc OUTPUTS: P, Q, R etc 1 1 1 1 1 1 1

Binary Logic Circuits A Q P B A B Q = A AND B P = NOT (A AND B) Learning Objectives: why data is represented in computer systems in binary form simple logic diagrams using the operations AND, OR and NOT truth tables combining Boolean operators using AND, OR and NOT to two levels. applying logical operators in appropriate truth tables to solve problems applying computing-related mathematics: +, -, /, *, Exponentiation (^), MOD, DIV Tips: Label the inputs on the circuit diagram Label the outputs on the circuit diagram Create a table with a column for each input and output Label the columns (outputs labelled in the form of an expression) Place the combinations of different zeros and ones in the input columns Workout the outputs for each output column in turn A Q P B A B Q = A AND B P = NOT (A AND B) INPUTS: A, B, C etc OUTPUTS: P, Q, R etc 1 1 1 1 1 1 1 1

What if there were 4 inputs? Binary Logic Circuits Learning Objectives: why data is represented in computer systems in binary form simple logic diagrams using the operations AND, OR and NOT truth tables combining Boolean operators using AND, OR and NOT to two levels. applying logical operators in appropriate truth tables to solve problems applying computing-related mathematics: +, -, /, *, Exponentiation (^), MOD, DIV Tips: When you place the combinations of different zeros and ones in the input columns…there are patterns that you can remember to help you… A B C 1 1 1 A B What if there were 4 inputs? 1 1 1 1 1 1 1 1 1 1 1 1 1 2 inputs 3 inputs

? ? Binary Logic Circuits This Lesson… Learning Objectives: why data is represented in computer systems in binary form simple logic diagrams using the operations AND, OR and NOT truth tables combining Boolean operators using AND, OR and NOT to two levels. applying logical operators in appropriate truth tables to solve problems applying computing-related mathematics: +, -, /, *, Exponentiation (^), MOD, DIV This Lesson… Binary Logic Circuit Expressions In your exam you will also be expected to be able to draw a diagram from an expression. ? A P ? B A B Q = A AND B P = NOT (A AND B) 1 1 1 How to we draw a diagram from an expression 1 1 1 1 1

Binary Logic Circuits A P B A B P Binary Logic Circuit Expressions Learning Objectives: why data is represented in computer systems in binary form simple logic diagrams using the operations AND, OR and NOT truth tables combining Boolean operators using AND, OR and NOT to two levels. applying logical operators in appropriate truth tables to solve problems applying computing-related mathematics: +, -, /, *, Exponentiation (^), MOD, DIV Binary Logic Circuit Expressions P = A AND (NOT B) ----BRACKETS FIRST!---- A 1st 2nd A P B B P

Binary Logic Circuits A P B A B P Binary Logic Circuit Expressions Learning Objectives: why data is represented in computer systems in binary form simple logic diagrams using the operations AND, OR and NOT truth tables combining Boolean operators using AND, OR and NOT to two levels. applying logical operators in appropriate truth tables to solve problems applying computing-related mathematics: +, -, /, *, Exponentiation (^), MOD, DIV Binary Logic Circuit Expressions P = NOT (A AND B) ----BRACKETS FIRST!---- A 1st 2nd A P B B P

Binary Logic Circuits A B P C A B C P Binary Logic Circuit Expressions Learning Objectives: why data is represented in computer systems in binary form simple logic diagrams using the operations AND, OR and NOT truth tables combining Boolean operators using AND, OR and NOT to two levels. applying logical operators in appropriate truth tables to solve problems applying computing-related mathematics: +, -, /, *, Exponentiation (^), MOD, DIV Binary Logic Circuit Expressions P = (A OR B) AND C ----BRACKETS FIRST!---- 1st 2nd A A B B P C C P

Binary Logic Circuits A P B A B P Binary Logic Circuit Expressions Learning Objectives: why data is represented in computer systems in binary form simple logic diagrams using the operations AND, OR and NOT truth tables combining Boolean operators using AND, OR and NOT to two levels. applying logical operators in appropriate truth tables to solve problems applying computing-related mathematics: +, -, /, *, Exponentiation (^), MOD, DIV Binary Logic Circuit Expressions P = (NOT A) AND B ----BRACKETS FIRST!---- 1st 2nd A A P B B P

Binary Logic Circuits A B P C A B C P Binary Logic Circuit Expressions Learning Objectives: why data is represented in computer systems in binary form simple logic diagrams using the operations AND, OR and NOT truth tables combining Boolean operators using AND, OR and NOT to two levels. applying logical operators in appropriate truth tables to solve problems applying computing-related mathematics: +, -, /, *, Exponentiation (^), MOD, DIV Binary Logic Circuit Expressions P = ((NOT B) AND C) OR A ----BRACKETS inside BRACKETS FIRST!---- 1st 2nd 3rd A A B B P C C P