邏輯閘：練習題

In a computer system, an edge-triggered D-type flip-flop is primarily used for which purpose?

A logic circuit is designed such that the output \(Y = \overline{A} + B\). Which combination of inputs will result in an output of 0?

In the construction of a full-adder, how many half-adders and what additional gate are typically used to produce the Sum and the Carry Out (\(C_{out}\))?

A specific logic gate produces a HIGH output (1) only when its two inputs are different. Which logic gate is being described?

A logic circuit consists of two inputs, A and B. Both inputs are connected to a single NOR gate. What is the Boolean expression for the output \(Q\) of this circuit?

State the Boolean expression for the output of a 2-input NAND gate with inputs \( X \) and \( Y \).

In a D-type flip-flop circuit, explain the effect of the clock signal in relation to the output \(Q\).

A logic circuit has three inputs: \( A, B, \) and \( C \). The output is defined as \( Q = (A \oplus B) \oplus C \). If all inputs are 1, what is the output \( Q \)?

A logic circuit is designed to control a safety alarm. The alarm (Z) should only be active (1) if the input A is high, and either input B or input C (but not both) is high.
a) Write the Boolean expression for this circuit.
b) How many rows would be in the truth table for this circuit?

Simplify the following Boolean expression using Boolean identities and De Morgan's laws:

\( Q = \overline{\overline{A} + \overline{B}} + (A \cdot \overline{B}) \)

Show your working for each step. (4 points)