Think about the following expression

If the number entered is greater than 15 but less than 25 or the number is 100 and the letter chosen is after p but less than Z and not the letter T or his name entered is greater than 4 characters and not “Steve” then say “Excellent” else say “Bogus!”

What would be the results for

1)11, Q, “Roger”2)100,T,”Bob”3)20,A,”Steve”

© GCSE Computing

Candidates should be able to: 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.

Slide 2

© GCSE Computing

The denary (decimal) system that we use has 10 digits (0-9). For a computer systems to use denary it would need to be able

to store and transmit 10 different ‘states’. It is therefore much simpler for computer systems to use the

binary number system because it has just 2 digits (0-1) which can easily be represented and stored as 2 different states.

Examples of different ‘states’ used to store/transmit binary data: ON / OFF (a semi-conductor switch, used in computer memory) TRANSMIT / DON’T TRANSMIT (an electrical signal, used to transfer

binary data) NORTH / SOUTH (areas with different magnetic polarity, used to

store binary data on magnetic media) REFLECT / NON-REFLECT (reflective and non-reflective areas, used

to store binary data on optical media)

Slide 3

© GCSE Computing

In computer science, the Boolean or logical data type is a data type that has two values (usually denoted true and false).

Logic gates are physical devices that can carry out Boolean logic functions.

The three basic logic gates are the AND, OR and NOT gates.

Slide 4

© GCSE Computing

The symbol for an AND gate is shown below. OUTPUT O is only true

if INPUT A AND INPUT Bare both TRUE.

This can be representedby this truth table.

It can also be representedby this logic statement:O = A AND B

An AND gate carries outBoolean multiplication (i.e. TRUE * FALSE = TRUE)

Slide 5

INPUTOUTP

UT

0 0 0

0 1 0

1 0 0

1 1 1

© GCSE Computing

The symbol for an OR gate is shown below. OUTPUT O is true

if INPUT A OR INPUT Bare TRUE.

This can be representedby this truth table.

It can also be representedby this logic statement:O = A OR B

An OR gate carries outBoolean addition (i.e. TRUE + TRUE = TRUE)

Slide 6

INPUTOUTP

UT

0 0 0

0 1 1

1 0 1

1 1 1

© GCSE Computing

The symbol for a NOT gate is shown below. OUTPUT O is true

if INPUT A is NOT TRUE. This can be represented

by this truth table. It can also be represented

by this logic statement:O = NOT A

A NOT gate carries outBoolean inversion (i.e. TRUE = FALSE)

Slide 7

INPUTOUTP

UT

0 1

1 0

© GCSE Computing Slide 8

A logic diagram is a diagram that represents one or more of logic gates linked together to form a logic circuit.

In logic diagrams; Symbols are used to represent logic gates Letters are used to label the input(s) and

output(s) Lines are used to show how logic gates are

connected.

© GCSE Computing Slide 9

In this logic diagram, the output will be FALSE only when inputs A and B are both TRUE.

This logic diagram can be written as a logic statement:

O = NOT (A AND B)

In this logic diagram, the output will be TRUE only when inputs A and B are both FALSE.

This logic diagram can be written as a logic statement:

O = NOT (A OR B)

In this logic diagram, the output will be TRUE only when input A is FALSE and input B is TRUE.

This logic diagram can be written as a logic statement: 

O = (NOT A) AND B

© GCSE Computing

INPUTOUTP

UT

A B O

0 0 1

0 1 1

1 0 1

1 1 0

Slide 10

INPUTOUTP

UT

A B O

0 0 1

0 1 0

1 0 0

1 1 0

INPUTOUTP

UT

A B O

0 0 1

0 1 0

1 0 0

1 1 0

© GCSE Computing Slide 11

For each logic diagram, complete a truth table and create a logic statement.

© GCSE Computing Slide 12

For each logic statement, complete a truth table and create a logic diagram.

O = (NOT A) AND (NOT B)

O = NOT (A OR (NOT B))

© GCSE Computing Slide 13

For each truth table, create a logic diagram and create a logic statement.

INPUTOUTP

UT

A B O

0 0 0

0 1 1

1 0 1

1 1 0

INPUTOUTP

UT

A B O

0 0 0

0 1 0

1 0 1

1 1 0