Final answer:
To identify if a month has 30 days, a microcontroller-based circuit with a user interface and programmed data on month lengths can be used. However, a simple circuit alone cannot determine this without programmable elements.
Step-by-step explanation:
To create a circuit that tells you whether a month has 30 days, you would need a programmable system, such as a microcontroller, that could store the lengths of different months. A simple tactile user interface could be used to input the month in question, and the system would light up an LED to indicate how many days are in that month based on a predefined program. Unfortunately, this task cannot be accomplished with a simple circuit alone without some form of programmability, as the data regarding the number of days in each month is not something that can be determined through simple electronic components like resistors, capacitors, and diodes.
If you were to create this as a more complex project, you could use a database or array within the programming of the microcontroller to store the number of days for each month. When the user inputs the month, the microcontroller would reference this data and illuminate an LED if the month has 30 days, or stay unlit if the month has 31 days (or 28/29 for February). The reference to the knuckle mnemonic can help in programming the correct number of days for each month.