Boolean Logic Flashcards

All 19 cards in this deck

What is a logic gate?

A circuit component that takes one or more inputs and produces a single output based on a logical function.

What shape is the AND gate symbol in a logic diagram?

A 'D' shape — a flat vertical edge on the left for the inputs and a semicircular curve on the right for the output.

What shape is the OR gate symbol in a logic diagram?

A curved (concave) left-hand edge with two curved sides meeting at a point on the right.

What shape is the NOT gate symbol in a logic diagram?

A triangle pointing right with a small circle (bubble) on its output; it has only one input.

When does an AND gate output 1?

Only when both of its inputs are 1; otherwise the output is 0.

True or false? An OR gate outputs 0 when both of its inputs are 1.

False. An OR gate outputs 1 when at least one input is 1, including when both are 1.

What does a NOT gate do to its input?

It inverts it: an input of 0 gives output 1, and an input of 1 gives output 0.

What is a truth table?

A table that lists the output for every possible combination of inputs to a gate or circuit.

What is a logic circuit?

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

Which symbols are used for AND, OR, XOR and NOT in Boolean expressions?

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

AND: $A . B$

OR: $A + B$

XOR: $A \oplus B$

NOT: a bar over the input, $\overline{A}$

In a truth table, what do 1 and 0 represent?

1 represents TRUE and 0 represents FALSE (they may also be written as T and F).

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

e.g. $Q = (A . B) + \overline{C}$

1. Draw the gates for the inner terms first: an AND gate with inputs A and B; a 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. $Q = A . \overline{B}$

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

2. Add a column for the first gate: $\overline{B}$ = 1, 0, 1, 0.

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

What are the steps to correct a logic circuit that produces the wrong output?

e.g. a circuit gives $Q = A + B$ but $Q$ should be 1 only when both inputs are 1

1. Write the Boolean expression for the circuit as drawn: $Q = A + B$
2. Write the expression the scenario or truth table requires: $Q = A . B$
3. Change the gate(s) that differ: replace the OR gate with an AND gate.

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.

How many rows of input combinations does a truth table need for a circuit with $n$ inputs?

$2^n$, e.g. 2 inputs need 4 rows and 3 inputs need 8 rows.

When does an XOR gate output 1?

When exactly one of its inputs is 1 (the inputs are different). It outputs 0 when both inputs are 0 or both are 1.

What shape is the XOR gate symbol in a logic diagram?

The OR gate shape with an extra curved line drawn across its inputs, just to the left of the curved input edge.