Boolean logic：練習問題

Identify the logic gate that produces an output of 0 ONLY when both of its inputs are 1.

Given the inputs \( A = 1 \) and \( B = 0 \), which of the following logic gates will produce an output of 1?

Which output sequence (for inputs AB in order 00, 01, 10, 11) correctly represents the Boolean expression \( X = \text{NOT } (A \text{ OR } \text{NOT } B) \)?

A logic circuit has two inputs, A and B. The output is 0 only when both inputs are the same (both 0 or both 1). Which single logic gate does this describe?

Which single logic gate is equivalent to the output of an AND gate being passed through a NOT gate?

Identify the single logic gate that produces an output of 0 only when both of its inputs are 1, and produces an output of 1 for all other input combinations.

A safety system uses a logic circuit with inputs S (Sensor) and K (Key). The alarm (X) activates if the sensor is triggered (S=1) OR if the key is NOT turned (K=0). Write the Boolean expression for the output X.

A logic circuit with three inputs \(X\), \(Y\), and \(Z\) produces an output \(Q\). The output \(Q\) is 1 only if (\(X\) is 1 AND \(Y\) is 1) XOR (\(Y\) is NOT 1 AND \(Z\) is 1). Write the complete Boolean logic expression for \(Q\) using the operators AND, XOR, and NOT.

State the Boolean expression and define the function for the following standard logic gates:

(a) AND gate (with inputs A and B)

(b) NOT gate (with input X)

(c) XOR gate (with inputs P and Q)

A simple safety monitoring system, S, outputs a signal (S=1) under the following conditions: the pressure (P) is too high (P=1) AND the temperature (T) is not high (T=0). Alternatively, the signal is triggered if the manual override switch (M) is activated (M=1).

(a) Write the Boolean expression for the output S in terms of P, T, and M.

(b) Draw the logic circuit corresponding to the expression derived in part (a). Use standard logic gate symbols.