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Logic Circuits and Boolean Expressions
This example is typical of AS exam questions which can be asked in four ways ...
- Given the boolean expressions, produce the circuit diagram and truth table.
- Given the circuit diagram, produce the boolean expressions and truth table.
- Given the truth table, produce the boolean expressions and circuit diagram.
- If Q is one when all the inputs are zero except for B, produce the truth table, the circuit diagram and the boolean expressions.
To understand this, you need to have a fair knowledge of the basics.
For the Falstad Circuit Simulation, CTRL+Click Example Logic Circuit
In options, check European Resistors and uncheck Conventional Current.
Click the logic inputs and watch the output change
Alternatively view Logic_Circuit.txt.
Save or copy the text on the web page. Import the saved or copied text into the Falstad simulator.
Here is the new HTML5 Simulator Site.
Creating the Truth Table
A B C D E Q
0 0 0 1 1 0
0 0 1 0 1 0
0 1 0 1 0 1
0 1 1 0 1 0
1 0 0 1 1 0
1 0 1 0 1 0
1 1 0 1 0 0
1 1 1 0 1 0
- Columns A, B and C count in binary from 0 to 7.
- This ensures that every combination of zeros and ones is present and in a sensible order.
- Column D (NOT Gate):
- This is produced by inverting column C (NOT Rule).
- The zeros become ones and the ones become zeros.
- Column E (NAND Gate):
- Look at columns B and D.
- Locate where two ones give a zero (NAND Rule).
- This happens in only two rows.
- All the other rows can be filled with ones without further thought.
- Column Q (NOR Gate):
- Look at columns A and E.
- Locate where two zeros give a one (NOR Rule).
- This happens in only one row.
- All the other rows can be filled in with zeros without further thought.
Q is ONE when all the inputs are zero except for B.
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