QB_PH_SEC8_028: Digital Electronics

A 4-bit asynchronous ripple counter is triggered by a periodic clock signal of frequency $f_{\text{in}} = 16.0\text{ MHz}$. What is the frequency (in MHz) of the output waveform at the final flip-flop ($Q_3$)?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Frequency Divider Action**: In a ripple counter, each flip-flop is clocked by the output of the preceding stage and toggles on active edges, dividing the frequency by 2: $f_{k} = \frac{f_{k-1}}{2}$ 2. **Total Division Ratio for 4 Stages ($n = 4$)**: $f_{\text{out}} = \frac{f_{\text{in}}}{2^n} = \frac{f_{\text{in}}}{2^4} = \frac{f_{\text{in}}}{16}$ 3. **Numerical Computation**: $f_{\text{out}} = \frac{16.0\text{ MHz}}{16} = 1.0\text{ MHz}$ 4. **Official Integer Answer**: 1.