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Logic CircuitsSituations to explain states What is a logic GateWhat is a Truth Table The three different gates Building Truth Tables
Situation Lets say your friends have asked you to go
to the cinema with them but your mum will only allow you to go if you have finished your homework and cleared up your room.
In this situation we have the following states 1. Homework done or homework not done2. Room cleared up and room not cleared up
We know that the states will effect the output of going to the cinema or not
DONE
NOT DONE
POSSIBLEOUTPUTS
INPUTS
Example Taking the example of above; lets
say you’ve done your homework but you have not cleared up your room… what would the output be?
DONE
NOT DONE
OUTPUTINPUT
S
States So from the above example we
could see that the states effect the output that we will receive.
As we already know a computer can only understand binary which is 1s (on) and 0s (off)
Hence logic gates are used to be able to conduct similar situations
What is a Logic Gate Logic gates are found in our computers
They are electronic devices used to control the flow of data
When data passes through a logic gate it changes its state, this change depends on the input
Many logic gates could be joined together to form a logic circuit, the function of this circuit is more complicated than a single logic gate
A Single Logic GateA single logic gate has the
following attributes 1. 1 or 2 inputs (if many gates are
joined you could have more inputs )
2. 1 single output 1 input and 1
output 2 inputs and 1
output
What is a Truth Table A Truth Table is basically the
table that shows all the possible inputs and the outputs of the logic gate
If we take the example of the cinema once again we would have the following table Homework Cleared Up Cinema
Not Done Not Done No
Not Done Done No
Done Not Done No
Done Done Yes
Truth Tables As we know computers will not
understand the truth table on the previous page… why is this?
A truth table from an actual computerised logic gate would look like the following
Homework
Cleared Up
Cinema
0 0 0
0 1 0
1 0 0
1 1 1
Comparing the two Truth Tables
Homework Cleared Up Cinema
Not Done Not Done No
Not Done Done No
Done Not Done No
Done Done Yes
Homework Cleared Up Cinema
0 0 0
0 1 0
1 0 0
1 1 1
Three Logic Gates We will now learn about three
different logic gates
We will be learning 1. The symbol used 2. The number of inputs3. Their truth tables 4. The different outputs
The NOT GateThe symbol for the NOT gate is
the following;
The NOT gate can only have ONE input and ONE output
A X
The NOT Gate Since computers only understand
1s and 0s there could be only two (21) possible inputs and outputs for this gate
The truth table shows this Input Output
A X0 11 0
Outputs The NOT gate basically outputs
the opposite of its inputs
Hence if the input is 1 the output would be 0
Example A good example is a switch as it
can either be on or off hence it can only have one input
01 1
01 0 0 1
The OR GateThe symbol for the OR gate is the
following;
The OR gate can only have TWO inputs and ONE output
A X
B
The OR Gate Since computers only understand
1s and 0s there could be four (22) possible inputs and outputs for this gate
The truth table shows this Input OutputA B X0 0 00 1 11 0 11 1 1
Outputs The OR gate only gives an output
of 1 if at least one of its inputs is 1
So if both inputs are 0 the output would be 0
but if both inputs are 1 the output would be 1
Example
The AND GateThe symbol for the AND gate is
the following;
The AND gate can only have TWO inputs and ONE output
A X
B
The OR Gate Since computers only understand
1s and 0s there could be four (22) possible inputs and outputs for this gate
The truth table shows this Input Output
A B X
0 0 0
0 1 0
1 0 0
1 1 1
Outputs The AND gate only gives an
output of 1 if both inputs are 1
So if an inputs 1 and the other input is 0 the output would be 0
but if both inputs are 1 the output would be 1
Example
Building a Truth TableLets say we want to draw a truth
table from the following logic circuit
A
B
C
Step 1Label all the possible outputs in
the logic circuit. In this case we have 3 inputs and there are 3 logic gates. Each logic gate’s output must be labeled;
D
E
F
Step 2Determine the possible number
of combinations. In this case it’s 23=8. So all the labels (both inputs and outputs are listed down with 8 spaces underneath each label).
A B C DA AND B
ENOT C
FD OR E
Step 3 Fill in the possible combinations
underneath the original inputs. Always start from the last input (C) with alternate 0s and 1s
A B C DA AND B
ENOT C
FD OR E
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Step 4The last step is to work the
resulting gatesA B C D
A AND B
E
NOT C
F
D OR E
0 0 0 0 1 1
0 0 1 0 0 0
0 1 0 0 1 1
0 1 1 0 0 0
1 0 0 0 1 1
1 0 1 0 0 0
1 1 0 1 1 1
1 1 1 1 0 1