Unit 10 T3 Boolean Logic part 1

Objectives

• Construct truth tables for the following logic gates:

• NOT, AND, OR
• NAND, NOR

• XOR (EOR)

• Create logic circuits from problem statements, logic
expressions or truth tables

• Complete truth tables from problem statements, logic
expressions or logic circuit
• Write logic expressions from problem statements, logic
circuits or truth tables

Multiple Select

Boolean Logic is a difficult topic

There are 2 lessons on this topic

There will be an exam on this topic after the 2 lessons.

How will you ensure you do well in this exam?

• Read the text and questions carfully

• Go back and Re-read any notes or slides before the question if you are stuck.

• Pay attention to any question you get wrong so you know the correct answer for next time.

• Just waste time by chatting with your neighbour.

Boolean logic

Unit 10 Advanced programming and databases

Starter

• Consider a safe with two keys

• If both keys are used, the safe opens

IF key1 AND key2
THEN
safeOpen <- TRUE

ELSE
safeOpen <- FALSE
ENDIF

• What are the only possible
values that key1 and key2 can be?

• What values must they be to open the safe?

Multiple Choice

What are the only possible values that key1 and key2 can be?

• Key1 and key2 can only be FALSE ( unlock)

• Key1 and key2 can only be TRUE (lock )

• Key1 and key2 can only be TRUE or FALSE (lock or unlock)

• Key1 and key2 can only be safeOpen = TRUE or safeOpen = FALSE

Boolean logic

Unit 10 Advanced programming and databases

Binary situations

• Binary situations are common in
daily life and can refer to things
that can be in only one of two
states:

• Stop or Go

• Pass or Fail

• On or Off

• In computing terms

• A binary 1 can represent TRUE

• A binary 0 can represent FALSE

Multiple Choice

What values must they be to open the safe?

• They must both be TRUE or FALSE to open the safe

• They must both be FALSE to open the safe

• They must both be TRUE to open the safe

• They must both be the same to open the safe

Boolean logic

Unit 10 Advanced programming and databases

Booleans in loops

• Booleans used in IF
statements and loops

WHILE doorOpen
turnOnLight()
ENDWHILE

Boolean logic

Unit 10 Advanced programming and databases

True or False?

Unlocking a smartphone:

• using a known fingerprint or

• using a correct PIN code?

IF fingerprint OR correctPIN
THEN
unlock <- TRUE

ELSE
unlock <-FALSE
end if

Multiple Choice

What would the first line of code be on bank vault unlock where the manager had to have the correct fingerprint and they should also show they know the PIN code.

• IF correctPIN or fingerprint

• IF fingerprint AND correctPIN

• IF fingerprint OR correctPIN

• IF fingerprint XOR correctPIN

Multiple Choice

What does this circuit diagram represent?

• AND
  Either switch needs to be down to complete the circuit

• OR
  Either switch needs to be down to complete the circuit

• AND
  Both switches must be down to complete the circuit

• OR
  Both switches must be down to complete the circuit

Multiple Choice

What does this circuit diagram represent?

• AND
  Either switch needs to be down to complete the circuit

• OR
  Either switch needs to be down to complete the circuit

• AND
  Both switches must be down to complete the circuit

• OR
  Both switches must be down to complete the circuit

Boolean logic

Unit 10 Advanced programming and databases

Truth tables

• A truth table shows the output from all possible
combinations of inputs from a Boolean expression

• If there are two inputs A AND B, there are four possible
combinations of TRUE and FALSE

• Both A and B must be True for the output to be True

Input A

Input B

A AND B

False

False

False

False

True

False

True

False

False

True

True

True

Multiple Choice

The below truth tables represent:

IF a lift is on the correct floor AND the call button has been pressed THEN open the lift door

What are the values for Open Lift Door and P below?

Multiple Choice

If lane one is open OR lane 2 is open then you can drive down the road

What is P?

Boolean logic

Unit 10 Advanced programming and databases

Boolean function – NOT

• IF the input is True then the output is False

• IF the input is False then the output is True

InputA

Output P = NOT A

False

True

True

False

Multiple Choice

What gate is this table for?

• AND
• OR
• NOT
• NOR

Multiple Choice

What gate is this table for?

• AND
• XOR
• OR 
• NOT

Multiple Choice

Which logic gate take the input and negates it, turning 0 to 1 and 1 to 0?

• AND

• OR

• NOT

Multiple Choice

This is the truth table for which logic gate?

• AND

• OR

• NOT

Multiple Choice

What is the output of an OR gate if its inputs are 0 and 0?

• 1

• 0

Boolean logic

Unit 10 Advanced programming and databases

More logic

Which of the following statements are True?

• (4 > 3) AND (5 > 7)

• (2 < 8) OR (8 > 10)

• NOT (5 * 7 > 30)

• ((7 DIV 3) >= 2) OR ((7 DIV 3) < 2)

• ((12 MOD 5) < 2) AND ((12 MOD 5) == 2)

• DIV gives the integer division (the result of division without any
fractional component)

• MOD gives the remainder after a division

Multiple Choice

Is this True or False?

(4 > 3) AND (5 > 7)

• True

• False

Multiple Choice

Is this True or False?

(2 < 8) OR (8 > 10)

• True

• False

Multiple Choice

Is this True or False?

NOT (5 * 7 > 30)

• True

• False

Multiple Choice

Is this True or False?

((7 DIV 3) >= 2) OR ((7 DIV 3) < 2)

(research DIV if you have forgotten)

• True

• False

Multiple Choice

Is this True or False?

((12 MOD 5) < 2) AND ((12 MOD 5) = 2)

(research MOD if you have forgotten)

• True

• False

Boolean logic

Unit 10 Advanced programming and databases

From truth tables to logic gates

• The following logic gates are used in circuits:

• AND gate

• OR gate

• NOT gate

• NAND gate (NOT AND)

• NOR gate (NOT OR)

• XOR gate (Exclusive OR)

Boolean logic

Unit 10 Advanced programming and databases

Binary logic – AND gate

• If both inputs are 1 (True) then the output is 1 (True)

• Otherwise the output is 0 (False)

Logic Diagram

Truth Table

INPUT
A

INPUT
B

OUTPUT
P

Logic statement: P = A AND B

A

B

P

0

0

?

0

1

?

1

0

?

1

1

?

Multiple Choice

Which is the correct Truth Table for AND

Boolean logic

Unit 10 Advanced programming and databases

Binary logic – OR gate

• If either input is 1 (True) then the output is 1 (True)

• Otherwise the output is 0 (False)

Logic Diagram

Truth Table

INPUT
A

INPUT
B

OUTPUT
P

Logic statement: P = A OR B

A

B

P

0

0

?

0

1

?

1

0

?

1

1

?

Multiple Choice

Which is the correct Truth table for OR?

Boolean logic

Unit 10 Advanced programming and databases

Binary logic – NOT gate

• If 0 is input it outputs 1 (True)

• If 1 is input it outputs 0 (False)

Logic Diagram

Truth Table

A

P

0

1

1

0

INPUT A

Logic statement: P = NOT A

OUTPUT P

Boolean logic

Unit 10 Advanced programming and databases

NAND, NOR and XOR gates

• A NAND gate gives the opposite results to an
AND gate

• It is the same as combining an AND gate with a NOT gate
• In the same way, a NOR gate is the same as combining an
OR gate with a NOT gate

• An Exclusive OR gate (XOR) will only be true if one
of the inputs is true

• It will be false if both inputs are true, hence it’s exclusive

• Complete the truth tables for NAND, NOR and
XOR gates

• Also, guess what the symbol would be for each

Match

Match the following

A XOR B

A NOR B

A NAND B

P = NOT A

AND

• A XOR B

• A NOR B

• A NAND B

• P = NOT A

• AND

Boolean logic

Unit 10 Advanced programming and databases

Worksheet 3

• Now complete Task Worksheet 3