battery voltage question

just brought out the express for the season tonight. When I went to start it the battery was quite weak from sitting and would barely roll over. I checked the voltage which was around 11.6v or so.

I hooked up the charger long enough to start it and went for a run around town for about a half an hour. When I went to start it, it again rolled over slow. I hooked up the charger again for about 2 hours while I cleaned up the garage.

once charged the battery shows about 12.6v or so when running and if I disconnect the alternator it shows about 12.4v (same voltage when the truck is shut off)

my question is most people I talk to tell me I should have 13 volts minimum when running and preferably over 13.5v. What do you think.....is the voltage to low and barely charging...

the dash guage shows positive when the alternator hooked up and negative when unhooked. The alt. is a 110 amp dual pulley one if it makes any diff.

thoughts fabo...........