digital electronics truth tables for several gates aberdeen grammar school
TRANSCRIPT
Digital Electronics
Truth tables for several gates
Aberdeen Grammar School
Drawing a truth table for a single gate is easy now.
We can look at the gate, and decide whether the output is high or low for each pair of inputs.A B Z
A
B
Z
0 0
0 1
1 0
1 1
0
1
1
1
This is the TRUTH TABLE for an OR gate
We also need to work out what the output is for digital circuits that have more than 1 logic gate
Is it possible to draw a truth table for this circuit?
Answer: YES!
But how many rows will our truth table have?
We also need to work out what the output is for digital circuits that have more than 1 logic gate
A
B
C
Z
Clue:
The number of rows in our table has to do with the number of inputs
How many rows did our 3 input AND gate we looked at have?
A B CA
B
C
Z
We will need 8 rowsZ
output
There is only one problem!
Filling out the output (ie the Z part) can be tricky…
A B CA
B
C
Z
Zoutput
So to make life easy, we add an extra letter to a mid point in the circuit.
D
A B CA
B
C
Z
D Zoutput
D
But now we need to include this letter in our truth table.
How can we do this??
A B CA
B
C
Z
D Zoutput
D
This circuit has only 1 mid point.
For every midpoint, we need an extra column.
Some circuits might have 2 or even 3 mid points.
We call this a ‘mid point’
A B CA
B
C
Z
D Zoutput
D
Now we fill out the left part as before, for the inputs.
Now we treat each part of D as a mini project!
We can basically OR, A with B to get D!
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
0
0
1
1
1
1
1
1
A B CA
B
C
Z
D Zoutput
D
Now look at the diagram above again.
What do we have to do now to get Z?
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
0
0
1
1
1
1
1
1
A B CA
B
C
Z
D Zoutput
D
It sometimes helps to cover up the columns we don’t need using a pencil or your hand.
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
0
0
1
1
1
1
1
1
We just AND ‘C’ with ‘D’ now.
0
0
0
1
0
1
0
1
A B CA
B
C
Z
D Zoutput
D
We now have a finished truth table for the circuit above!
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
You will now try some examples on your own.