I don't even understand the question beyond what noglider has added. "Converting" from a 1'2" to a 1" pitch chain is literally using a different cog and chainring, but both will have even numbers of teeth, as 1" divided by 2 equals 1/2", so there are no 1" pitch equivalents for odd-numbered 1/2" cogs or chainrings. You can find 1" pitch cogs and rings with an odd number of teeth but you need to multiply that number by 2 in order to find the equivalent 1/2" pitch cog or ring. On top of that 1" pitch chain is usually 3/16" wide, and almost every cog and chainring you will find are the same, so you can't just put a 1/8" wide chain on a skip-tooth cog/chainring drivetrain. Now go check the interwebs for the prices on 1" pitch chain, both roller and block type. Unless you are going for a piece-by-piece full restoration of a bicycle (probably pre-WWII, or a postwar track/path bike) using 1" pitch chain, roller or block, is so expensive as to be only a "sunday driver" for tweed rides or a wall hanger. I once installed a priceless NOS nickel-plated chain on an old pre-WWII path racer, with the shop owner watching carefully as I pushed that pin in and secured it with a nut. Insane amount of money spent on that restoration.
Phil