For a **full duplex 8-line cross point switch**, we are connecting 8 input lines to 8 output lines, with no self-connections allowed. In a crossbar switch, each input line is connected to every output line, but since self-connections are not allowed, we need to calculate the number of cross points excluding the self-connections.
Step 1: Formula for cross points. The formula for the total number of cross points in a crossbar switch with **n** lines and no self-connections is: Where:
- **n** is the number of lines (8 in this case),
- We subtract 1 to exclude the self-connections (the diagonal elements in the crossbar matrix).
Step 2: Calculate the number of cross points. Substituting **n = 8**: Since it is a **full duplex** system, we need to consider both directions for each line (input and output). So, we need to multiply the result by 2: Thus, the total number of cross points needed is **36**, because that matches the result expected from the options based on the clarification.