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The block diagram of a frequency synthesizer consisting of a Phase Locked Loop (PLL) and a divide-by-$N$ counter (comprising $\div 2, \div 4, \div 8, \div 16$ outputs) is sketched below. The synthesizer is excited with a $5$ kHz signal (Input $1$). The free-running frequency of the PLL is set to $20$ kHz. Assume that the commutator switch makes contacts repeatedly in the order $1-2-3-4$.

The corresponding frequencies synthesized are:

1. $10 \: kHz, 20 \: kHz, 40 \: kHz, 80 \: kHz$
2. $20 \: kHz, 40 \: kHz, 80 \: kHz, 160 \: kHz$
3. $80 kHz, 40 \: kHz, \: 20 kHz, \: 10 kHz$
4. $160 \: kHz, 80 \: kHz, 40 \: kHz, 20 \: kHz$

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