O.K. : Hondas simple and excellent CDI ignition system has a separate coil inside the alternator that sends a signal to the pickup, this shoots a quick jolt to the ignition coil and ignition control box .
Some times metal SWARF (filings, debris, normal wear particles) accumulate on the fixed magnets in the alternator's rotor .
I don't want you to take it all apart, I don't know how to tell you how to test it but I'm sure if you google 'Honda CT110 ignition testing' or maybe 'Honda single CDI testing', some thing along those lines, will have a detailed post on *exactly* your system .
I recently had a serious mid range cutting out problem and was
SURE it was electrical as most "carburator problems" are in fact electrical faults .
So, I kept fooling with it, no joy so I "shotgunned" the entire ignition system using $pendy New Old $tock factory parts, guess what ? it ran no better
(I couldn't find the hair pulling emoticon) , in desperation I took it to my friend who owns a Honda Moto dealership, he tinkered with it and said 'it all looks O.K. to me apart from that brand new CHINES carby ! I hate them !' .
It took me a month and $320.00 to find the correct, N.O.S. HONDA KEI-HIN made in Japan
PD27 carby, it was in
Palistan for goodness sake, I bought it and slapped it on, the bike started easily and ran / rode *perfectly* , as of yet I've not even adjusted the idle mixture .
It's wierd as I didn't often see a spark when testing it by kicking it vigorously with the plug out and on the cylinder head but apparently it did have spark the whole time .
The system is shut off by grounding the low tension side of the ignition coil .
I dunno if this is helpful, others here prolly know more than I about this system 35 years ago I was given a late model CT110 with no wheels, it had a single wire ignition coil and I had to fool with it for several days before it suddenly had decent blue / white sparks and the engine began to run .