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 0

2. Convert the same numbers to hex

3. Convert these hex numbers to binary

A 3 4 F 2 4 2 9

4. Convert these binary numbers to hex

0 1 1 1 0 0 0 1 1 0 1 1 0 1 0 1

5. 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 specification

Recap on binary numbers

AND OR NOT

Truth tables

Logic diagrams

Logic.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 as

A . 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 as

A + 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 sheet

As a minimum, do AND, NOT and OR

Extension – try the remaining ones

Using Logic.Ly

Go to http://logic.ly/ and select Try Online

Close the demo box offered

Drag the gates and inputs and outputs to the main window

Try to build and AND, NOT and an OR circuit

Try these circuits: Circuit 1

Circuit 1

0

1

1

1

1

0

0

0

Circuit 2

Circuit 2

0

0

0

1

1

1

1

0

Circuit 3

Circuit 3

0

1

1

1

1

0

1

0

0

0

1

0

Circuit 40

00

0

0

0

0

0

0

0

0

0

1

1

1

1

0

00

1

0

0

0

1

0

0

0

1

0

0

0

1

0

00

1

0

0

0

1

0

0

0

1

1

1

1

1

Circuit 5

1

1

0

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

0

1

1

1

0

1

1

1

0

1

1

1

1

1

0

0

1

0

0

0

0

0

Circuit 6

0

0

0

0

1

1

1

1

0

0

1

1

0

0

1

1

0

1

0

1

0

1

0

1

1

1

0

0

1

1

0

0

0

0

0

0

0

0

1

1

0

1

0

0

0

1

0

0

0

1

0

0

0

1

1

1

1

0

1

1

1

0

0

0