Question E7A03:
Which of the following can divide the frequency of a pulse train by 2?  

Choices:  
A: An XOR gate  
B: A flip-flop  
C: An OR gate  
D: A multiplexer    

Correct Answer is  B: A flip-flop  

A flip-flop divides a pulse train by 2 when configured to toggle on every clock edge (e.g., T flip-flop with T=1, JK with J=K=1, or a D flip-flop with $\overline{Q}$ fed back to D). Each clock edge inverts the output, so the output period doubles (frequency halves).

- Correct: B: A flip-flop  
  - Each clock edge toggles the state, so:
    $$f_{out} = \frac{f_{in}}{2}$$
  - Produces a near 50% duty cycle when triggered on one edge.

Why the others are incorrect:
- A: XOR gate  
  - Purely combinational; no memory. Cannot divide frequency by itself.
- C: OR gate  
  - Also combinational; cannot create a lower-frequency output from a single input pulse train.
- D: A multiplexer  
  - Selects among inputs; without state it cannot perform frequency division.

Useful rules of thumb:
- One toggle flip-flop: $f_{out} = \frac{f_{in}}{2}$.
- Cascade $N$ flip-flops to build a binary divider (ripple counter):
  $$f_{out} = \frac{f_{in}}{2^N}$$
- Combinational logic (AND/OR/XOR/MUX) cannot divide frequency without added state (storage).