1. Digital Electronics Truth tables for several gates Aberdeen Grammar School

2. 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. ABZ A B Z 0 0 1 1 0 1 0 1 1 1 This is the TRUTH TABLE for an OR gate

3. 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?

4. 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?

5. ABC A B C Z We will need 8 rows Z output There is only one problem! Filling out the output (ie the Z part) can be tricky…

6. ABC A B C Z Z output So to make life easy, we add an extra letter to a mid point in the circuit. D

7. ABC A B C Z DZ output D But now we need to include this letter in our truth table. How can we do this??

8. ABC A B C Z DZ output 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’

9. ABC A B C Z DZ output 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

10. ABC A B C Z DZ output 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

11. ABC A B C Z DZ output 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

12. ABC A B C Z DZ output 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.