Thanks. That's a nice score you got there. Your saw is a late production 1050 that would have come from Homelite with the SDC carb setup (and I can tell from the brass blockoff plugs on the carb box that it's set up that way now). Notice how your carb box doesn't have the grommet and hole for the third needle (idle adjust) like the saw I worked on has.
Here you can see the hole and grommet for the third needle (which this saw had when it was Tillotson HL equipped). Somebody must have installed the SDC 'retrofit' kit on this saw.
Your saw also has the paint scheme and decals associated with a late 1050 (my buddy bought one just like yours new in 1986 or so). When you rebuild that carb, do yourself a favor and unbolt the carb manifold from the carb box so you can tilt the manifold/carb assembly up and easily reach the carb attchment screws. Otherwise, there's just no damn way to tighten the left side screw. An ignition wrench won't fit around it (because of the 'spitback' tube) and you can't get a straight shot with a screwdriver because of interfereance with the back of the carb box. When you remove the manifold you may have to replace the gasket that goes between it and the reed cage. That is a Tillotson HL carb flange gasket.
Looks like this:
38-1555 - Tillotson 16B-206 Hl Intake Gasket | Chain Saw Parts | MFG Supply
The OEM Homelite gasket looks like this:
HOMELITE CHAINSAW VINTAGE 1050 1130 INTAKE GASKET 63655 | eBay
Either will work. Most K10-SDC carb rebuild kits don't come with a carb mounting gasket. You'll either have to reuse your old one, make a new one, or buy one. This is what the Homelite gasket looks like:
HOMELITE NEW SUPER XL 925, SUPER XL 925W CARB GASKET | eBay
Any Tillotson HS or Walbro SDC carb mounting gasket will work, so long as the impulse hole is in the right place. Here's the Tillotson HS application gasket:
38-3656 - Tillotson 16B-228 HS Intake Gasket | Chain Saw Parts | MFG Supply