Combining Boolean Operators Flashcards

All 7 cards in this deck

What is a logic circuit?

Two or more logic gates connected together, where the output of one gate can become an input to another.

What symbols can be used for AND, OR and NOT in Boolean expressions?

e.g. A AND B, A OR B, NOT A

AND: $A \land B$ or $A.B$

OR: $A \lor B$ or $A+B$

NOT: $\lnot A$, $\sim A$ or $\bar{A}$

True or false? In a truth table, T and F may be used instead of 1 and 0.

True. Other valid notation is accepted in the exam, with T = 1 (TRUE) and F = 0 (FALSE).

What are the steps to draw a logic diagram from a Boolean expression?

e.g. $Q = (A \land B) \lor \lnot C$

1. Draw the gates inside the brackets/inner terms first: AND gate with inputs A and B; NOT gate with input C.

2. Feed both of those outputs into the final gate: an OR gate.

3. Label the final output: Q.

What are the steps to complete a truth table for a circuit with two gates?

e.g. $Q = A \land \lnot B$

1. List every input combination of A and B: 00, 01, 10, 11.

2. Add a column for the first gate: NOT B = 1, 0, 1, 0.

3. Apply the final gate to get Q: 0, 0, 1, 0 (so Q = 1 only when A=1, B=0).

What are the steps to design a logic circuit for a scenario?

e.g. an alarm sounds when the sensor is triggered and the system is armed

1. Identify the inputs: A = sensor triggered, B = system armed.

2. Match the wording to gates: 'and' → AND gate ('or' → OR, 'not' → NOT).

3. Draw and label the gates and output: $Q = A \land B$.

How do you edit a logic diagram whose output is correct except that every value is the opposite of the one required?

e.g. the diagram gives 1 for every row where the truth table needs 0

Add a NOT gate to the output of the final gate.

It inverts every output, so 1 becomes 0 and 0 becomes 1.