To answer this question, we need to understand how a multiplexed LED matrix works and how to determine the number of independent light-emitting nodes and the microcontroller control pins required.

Understanding a Multiplexed LED Matrix

A multiplexed 6 by 4 LED matrix is a grid of LEDs arranged in 6 rows and 4 columns. The total number of independent light-emitting nodes is the product of the number of rows and columns.

Calculations for the total independent nodes:

• Number of rows: 6
• Number of columns: 4
• Total light-emitting nodes = 6 * 4 = \(24\)

Hence, the total number of independent light-emitting nodes in the matrix is 24.

Determining Necessary Microcontroller Control Pins

For a multiplexed LED matrix, you need to control each row and each column separately, which typically requires one control pin per row and one per column.

Calculations for control pins:

• Control pins for rows: 6
• Control pins for columns: 4
• Total control pins required = 6 + 4 = \(10\)

Therefore, a minimum of 10 microcontroller control pins are required to operate a 6 by 4 LED matrix.

Conclusion

From the calculations, we conclude that:

• The total number of independent light-emitting nodes is 24.
• The minimum number of microcontroller control pins needed is 10.

Based on the explanation above, the correct answer is: 24; 10.