Mastering Loops
Mastering Logic Gates and Truth TablesWhat is Boolean?Logic
Gates TypesCorresponding Truth tablesDrawing circuit diagrams
VIDEOS included (demos of logic gate) using logic.ly/demo*Also see
presentations on boolean logic
Purchase the full teaching package (KS3, GCSE and A Level topics
from www.teachingcomputing.com Did you know?Have you ever looked
inside your computer? The internal circuitry of computers is a bit
of a mystery. Have a look at the mother board on the right. Logic
Gates play a big role in understanding the circuitry of computers.
Digital systems are basically constructed using logic gates that
operate using Boolean logic
Source: Wires N Code
An Electronics Project WebsiteWhat is Boolean?!In computer
science, the Boolean data type is a data type, having two values
(usually denoted true (1) and false (0), intended to represent the
truth values of logic and Boolean algebra. It is named after George
Boole, who first defined an algebraic system of logic in the mid
19th century.Example: Data type: Seat booked? Options are True (1)
or False (1)
and what is a logic gate?In electronics, a logic gate is an
idealized or physical device implementing a Boolean function; that
is, it performs a logical operation on one or more logical inputs,
and produces a single logical output.Logic gates are primarily
implemented using diodes or transistors acting as electronic
switches, but and this is interesting - can also be constructed
using vacuum tubes, electromagnetic relays (relay logic), fluidic
logic, pneumatic logic, optics, molecules, or even mechanical
elements.
Logic circuits include such devices as ALUs*, computer memory,
and complete CPU** chips, which may contain more than 100 million
gates*Arithmetic Logic Units**Central Processing Unit (the brain of
the computer)4Logic Gates and CircuitryLearning about logic gates
will give you an insight into the circuitry of computers and how
they work.
Youll remember that computers dont understand English all they
can make sense of is: Binary (0) and (1) as computers are basically
comprised of millions of on and off switches.In modern practice,
most gates are made from field-effect transistors (FETs),
particularly MOSFETs (metaloxidesemiconductor field-effect
transistors).5Hardware Design how would you illustrate a circuit
with its components?If you tried to draw the circuit on the right
on paper (as it is) it probably wouldnt make much sense. Common
convention uses a series of symbols to stand for the various types
of logic gates. The diagram on the right is a circuit diagram
showing 3 inputs and 2 outputs. You can combine logic gates to do
clever things with inputs and outputs.But what do the funny shapes
mean?
You may understand what it means because its your circuit, but
other people would struggle!
6Types of GatesIf you are a beginner to all this, you probably
would start with knowing the three main gates: the AND gate, the OR
gate and the very clever NOT gate. The symbolic representations for
each of these gates is shown below.AndOrNot
Yes, it would be helpful if the AND and OR gates didnt look
quite so similar, but thats just the way it is now. You would do
well to find an interesting way of remembering what the AND and OR
gates look like, and test yourself to make sure you dont get
confused.
7The And Gate remembering the shape!And
Memory by association really works. The wackier and more
creative the association the more likely you are to remember what
the gates stand for! Heres one (completely ridiculous way but it
worked for me) Try and think of your own!This gate is ROUNDED and
looks a little like the door of a cave (if rotated). A year ago I
was in a desert there was loads of SAND, and there were caves
nearby in which the (biblical) dead sea scrolls were found.
AND!
8The Or Gate remembering the shape!OrMemory by association
really works. The wackier and more creative the association the
more likely you are to remember what the gates stand for! Heres one
(completely ridiculous way but it worked for me) Try and think of
your own!Thor was a chap that was from space. The gate above looks
a little like a space ship. THOR .from outer space, and so when I
see a spaceship shaped gate, I think: THOR.and remember its the OR
gate.
9Other types of gatesThere are other types of gates which make
use of the AND or OR symbolic representations within them
NANDNORXORXNOR10What do these gates do?Watch the video below, or
create the diagram for yourself in logic.ly/demo and see what
happens. Note that the gate below is the AND gate.
Connect the toggle switches (on the left) to the AND gate
(centre) and then the AND gate to the bulb (output)Youll notice
something quite interesting: The bulb only lights when both Input 1
AND Input 2 are on. The AND logic gate performs this function and
produces an output depending on the inputs. If INPUT A = 1 (on) and
INPUT B = 1 (on),Only then with the output also be on (1)Input
AInput BIf Input B is ON (this represents a 1)If InputA AND InputB
are on, then the bulb will be on (Boolean value = 1)AND GATE11
What do these gates do?Watch the video below, or create the
diagram for yourself in logic.ly/demo and see what happens. Note
that the gate below is the OR gate. Connect the toggle switches (on
the left) to the OR gate (centre) and then the OR gate to the bulb
(output)Youll notice something quite interesting: The bulb lights
up when either Input 1 OR Input 2 are on. The OR logic gate
performs this function and produces an output depending on the
inputs. If INPUT A = 1 (on) OR INPUT B = 1 (on),the output also be
on (1)Input AInput BIf Input B is ON (this represents a 1)If InputA
OR InputB are on, then the bulb will be on (Boolean value = 1)OR
GATE12 The NOT gate acts as an inverterWatch the video below, or
create the diagram for yourself in logic.ly/demo and see what
happens. Note that the gate below is the NOT gate. Connect the
single input (toggle switch on the left) to the NOT gate, and then
connect the NOT gate to the bulb.Youll notice a pattern. If the
switch is on (1) then the bulb is off (0). And if the switch is off
(0), then the bulb goes on (1)The NOT gate tends to invert the
signal that is coming through to produce the opposite signal. If
INPUT A = 1 then NOT A = 0If INPUT A = 0 then NOT A = 1Input AInput
BIf Input B is ON (this represents a 1)If InputA OR InputB are on,
then the bulb will be on (Boolean value = 1)NOT GATE
Input ANOT GATEIf Input A = 0 (off) then the bulb is on!13Use of
a truth table weird examplesEach of the gates have a corresponding
TRUTH TABLE. The truth table is an effective way of displaying the
inputs and outputs of a gate using binary (Boolean values)Variable
AVariable BFinal OutputX is goodX is divineBelieve!X is not goodX
is divineDont believe!X is goodX is not divineDont believe!Suppose
the desired outcome was to PUT YOUR FAITH in Person x. You may come
up with two factors that are crucial in determining whether or not
you should put your faith in this person. Variable A = X must be
Good ANDVariable B = X must be DivineYoull note that you have made
use of an AND gate - both conditions must be true for the output to
be favourable.14Another example this time for the ORAchieved an
AAchieved a BGoing on Trip?NoNoNopeYesYesYes!NoYesYes!YesNoYes!Your
computing teacher is planning a trip to Bletchley Park. It is only,
unfortunately, for the students that managed to achieve an A OR a B
in their A Level Exams. What would the truth table look like?Youll
note that you have made use of an OR gate - EITHER CONDITION can be
true for a favourable response. 15Using truth tablesEach of the
gates have a corresponding TRUTH TABLE. The truth table is an
effective way of displaying the inputs and outputs of a gate using
binary (Boolean values)And
ABA*BNote: The And gate is associated with
multiplication????16Using truth tablesEach of the gates have a
corresponding TRUTH TABLE. The truth table is an effective way of
displaying the inputs and outputs of a gate using binary (Boolean
values)Or
ABA+BNote: The OR gate is associated with addition????17Using
truth tablesEach of the gates have a corresponding TRUTH TABLE. The
truth table is an effective way of displaying the inputs and
outputs of a gate using binary (Boolean values)Not
ANot A??18Using truth tablesThis is a NOT-AND gate which is
equal to an AND gate followed by a NOT gate. The outputs of all
NAND gates are high ifanyof the inputs are low. The symbol is an
AND gate with a small circle on the output. The small circle
represents inversion.
NAND
AB__AB????19Using truth tables
NORThis is a NOT-OR gate which is equal to an OR gate followed
by a NOT gate. The outputs of all NOR gates are low if any of the
inputs are high.The symbol is an OR gate with a small circle on the
output. The small circle represents inversion
AB____A+B
????20Using truth tablesThe 'Exclusive-OR' gate is a circuit
which will give a high output if either, but not both, of its two
inputs are high. An encircled plus sign () is used to show the EOR
operation.
XOR
AB
????21Using truth tablesThe 'Exclusive-NOR'gate circuit does the
opposite to the EOR gate. It will give a low output ifeither, but
not both, of its two inputs are high. The symbol is an EXOR gate
with a small circle on the output. The small circle represents
inversion.
XNOR
AB
????22Sample Questions
*taken with permission from OCR (Specimen paper)23Sample
Questions
*taken with permission from OCR (Specimen paper)24Sample
Questions
*taken with permission from OCR (Specimen paper)25Answers
*taken with permission from OCR (Specimen paper)26