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, 8 input lines are connected to 8 output lines, excluding self-connections. In a crossbar switch, each input connects to every output. With self-connections disallowed, we must exclude these diagonal connections when calculating the total cross points.

Step 1: Formula for cross points. The formula for total cross points in a crossbar switch with n lines, excluding self-connections, is:\[\text{Cross points} = n \times (n - 1)\]Where:- n represents the number of lines (8 in this scenario).- Subtracting 1 from n excludes self-connections (the diagonal elements of the crossbar matrix).

Step 2: Calculate the number of cross points. Substituting n = 8 into the formula:\[\text{Cross points} = 8 \times (8 - 1) = 8 \times 7 = 56\]As this is a full duplex system, both directions for each line (input and output) must be accounted for. Therefore, the result must be multiplied by 2:\[\text{Full duplex cross points} = 56 \times 2 = 112\]Consequently, the total number of cross points required is 112, aligning with the expected result based on the provided options and clarification.