You are in a laboratory at the top of a mountain 100 miles away from a base station. There are two links with the base station: a microwave link that transmits data at the speed of light and a wire link that transmits data at two thirds the speed of light. You decide to transmit a common data stream using both media for security. Because of the difference in transmission speeds, the base station receives the microwave data earlier than the cable data. Suppose you decide to perform some error processing on the microwave data before comparing with the cable data, how many operations can you perform if each operation takes 2 ns?

What will be an ideal response?

The distance of the transmission path is 100 miles or 160,900 meters. If the speed of light is 3.0 × 108 m/s, the transit time by radio is 16.09 × 104/3.0 × 108 = 5.36 × 10?4s.

The wire link takes one third longer, that is 0.33 × 5.36 × 10?4 = 1.77 × 10?4 s. If computing operations can take place at the rate of one every 2 ns, the number of operations (on the radio signal) that could take place before the wire signal arrives is 1.77 × 10?4/(2 × 10?9) = 8.85 × 104 = 88,500.