How to create binary variable if two columns fit within normal working hours?

I have a df:

Date       Time
06/20/20   1740
02/19/20   1600
09/22/20   1530
12/09/20   1326
06/12/19   1119
07/19/19   1703
08/02/20   1805
12/05/19   0932
11/09/20   1134
01/14/20   1634

The times are listed in military time. I would like to create a data frame that has a third variable (working_hours) that is a binary. If the date is a Monday through Friday and the Time is between 0900 and 1700 then I'd like a 1, otherwise 0. I'd also like to make a variable, Morning, for if the time is before or after noon (1200). Any thoughts?

Output:
    Date       Time   Working_Hours   Morning
    06/20/20   1740   0               0
    02/19/20   1600   1               0
    09/22/20   1530   1               0
    12/09/20   1326   1               0
    06/12/19   1119   1               1
    07/19/19   1703   0               0
    08/02/20   1805   0               0
    12/07/19   0932   0               1
    11/09/20   1134   1               1
    01/12/20   1634   0               0