1. clearScreen(): Clears the display screen of the calculator, resetting it to zero.

2. appendToScreen(value): Appends the specified value to the display screen of the calculator. It handles adding numbers, operators, and decimal points.

3. appendOperator(operator): Appends the specified operator to the display screen of the calculator, ensuring that operators are added correctly based on the last character on the screen.

4. calculate(): Evaluates the expression displayed on the screen and displays the result.

5. calculateSquareRoot(): Calculates the square root of the number displayed on the screen and displays the result.

6. calculateBinary(): Converts the number displayed on the screen to its binary representation and displays the result.

7. calculateOctal(): Converts the number displayed on the screen to its octal representation and displays the result.

8. displayMonthlyCalendar(): Displays a monthly calendar based on the date entered in the calculator. It extracts the year and month from the entered date and generates a calendar table for that month.

9. calculateSin(): Calculates the sine of the angle (in degrees) displayed on the screen and displays the result.

10. calculateCos(): Calculates the cosine of the angle (in degrees) displayed on the screen and displays the result.

11. calculateTan(): Calculates the tangent of the angle (in degrees) displayed on the screen and displays the result.

12. displayClock(): Updates the clock display with the current time, showing hours, minutes, and seconds.

13. toggleClock(): Toggles the visibility of the clock and alarm elements. If the clock is hidden, it becomes visible along with the alarm input; otherwise, they are hidden. It also starts or stops the clock interval based on visibility.

14. setAlarm(): Sets an alarm for the specified time entered by the user. If the current time matches the alarm time, it triggers an alert.

The above calculator performs the following operations:

1. Basic Arithmetic Operations: Addition (+), Subtraction (-), Multiplication (*), and Division (/).

2. Exponentiation: It supports raising a number to a power (^).

3. Square Root: It calculates the square root (√) of a number.

4. Trigonometric Functions: It computes the sine (sin), cosine (cos), and tangent (tan) of an angle measured in degrees.

5. Binary and Octal Conversion: It converts a decimal number to its binary (BIN) and octal (OCT) representations.

6. Calendar Display: It generates and displays a monthly calendar based on the entered date.

These operations cater to basic arithmetic calculations, trigonometric functions, and conversions between different number systems, providing a versatile set of functionalities for mathematical calculations.