If you BAN someone are they Baned??? NO! BaNNed. double N
If you are a bum are you Buming around??? NO! BuMMing around!
If you get a tan bathing are you Taning Yourself?? NO! Tanning……

The list goes on. If a vowel comes before the last letter then you must add the extra letter or you change the sound.

Banned spelt BANED would be pronounced BAYNED.
Bumming spelt BUMING would be pronounced BOOMING.
Tanning spelt TANING would be pronounced TAYNING.

AND PROGRAMING IS PRONOUNCED PROGRAYMING….. GET IT.

Americans you use this rule for every other example so why just change an entire rule for 1 word. If im wrong and you have a different rule please correct me.
AMERICA the rest of the world already thinks your stupid…Stop making it so easy for us to dislike you. I want to like you… You just dont make it easy sometimes.

1.
a. A listing of the order of events and other pertinent information for a public presentation.
b. The presentation itself: a program of piano pieces.
2. A scheduled radio or television show.
3. An ordered list of events to take place or procedures to be followed; a schedule: a program of physical therapy for a convalescent.
4. A system of services, opportunities, or projects, usually designed to meet a social need: “Working parents rely on the center’s after-school latchkey program” (New York Times).
5.
a. A course of academic study; a curriculum.
b. A plan or system of academic and related or ancillary activities: a work-study program.
c. A plan or system of nonacademic extracurricular activities: the football program.
6. A set of coded instructions that enables a machine, especially a computer, to perform a desired sequence of operations.
7. An instruction sequence in programmed instruction.

I would definitely spell definitions 1 and 2 “programme,” 3, 4, and 5 “programme” or “program” (I’ll pick one eventually!), and 6 and 7 would definitely be spelt “program” as with the verb form of “program.”