Teaching Computing to GCSE Level with PythonSession 3

Your second starter!1. Convert these binary numbers to denary:0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 02. Convert the same numbers to hex3. Convert these hex numbers to binaryA 3 4 F 2 4 2 94. Convert these binary numbers to hex0 1 1 1 0 0 0 1 1 0 1 1 0 1 0 15. What is the largest denary number you can express in 9 bits?6. How many different values can you show using 9 bits?

Topics for todayTheory

Binary logic: AND, OR, NOT Truth tables Logic Gates www.logic.ly

Programming IF Statements

Binary logicGCSE Computing link to specificationRecap on binary numbersAND OR NOTTruth tablesLogic diagramsLogic.ly

Link to specification(OCR GCSE Computing Specification)

Candidates should be able to:

(d) explain why data is represented in computer systems in binary form

(e) understand and produce simple logic diagrams using the operations NOT, AND and OR

(f) produce a truth table from a given logic diagram.

(a, b and c are points that relate to the CPU)

AND OR NOT For A AND B to be true, then A must be true and B must be true For example, “It is true that Cambridge United won last week and there was 5 cm

of snow on Friday” is only true if both are true. For A OR B to be true then at least one of A and B must be true “It is true that Cambridge United won last week OR there was 5 cm of

snow on Friday” is true if only one of the individual statements is true

NOT A is always the opposite of A. So if A is true, NOT A is false. For example, “It is not raining” is true if “It is raining” is false

The NOT gate (inverter)

Note there is 1 input, A, and 1 output (often called Q)We can also represent this mathematically as

Diagrammatic representation of a NOT gate

Athe bar notation represents logical NOT

A

The AND gate

Note there are 2 inputs, A and B, and 1 output Q

We can also represent this mathematically asA . B

(the dot notation represents logical AND)

Diagrammatic representation of an AND gate

The OR gate

Note there are 2 inputs, A and B, and 1 output Q

We can also represent this mathematically asA + B

(the + notation represents logical OR)

Diagrammatic representation of an OR gate

Truth Tables

A truth table shows the output values for all the different input combinations.

TaskComplete the truth tables on the sheetAs a minimum, do AND, NOT and ORExtension – try the remaining ones

Using Logic.Ly

Go to http://logic.ly/ and select Try OnlineClose the demo box offeredDrag the gates and inputs and outputs to the main

windowTry to build and AND, NOT and an OR circuit

Try these circuits: Circuit 1

Circuit 1

0111

1000

Circuit 2

Circuit 2

0001

1110

Circuit 3

Circuit 3

0111

1010

0010

Circuit 40000000000001111

0001000100010001

0001000100011111

Circuit 5

11001100

00000011

11011101

11011111

00100000

Circuit 6

00001111

00110011

01010101

11001100

00000011

01000100

01000111

10111000