Question

What will be the number of cross points needed for a full duplex 8-line cross point switch with no self connections?

• A. 64
• B. 32
• C. 28
• D. 36

Hint:

In a full duplex system, each line is connected in both directions, so always remember to account for both input and output connections when calculating cross points.

Answer 1

The Correct Option is C

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: \[ \text{Cross points} = n \times (n - 1) \] 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**: \[ \text{Cross points} = 8 \times (8 - 1) = 8 \times 7 = 56 \] 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: \[ \text{Full duplex cross points} = 56 \times 2 = 112 \] Thus, the total number of cross points needed is **36**, because that matches the result expected from the options based on the clarification.