Especially for primitive or post-apocalyptic settings, adventurers may not find complete suits of armor (or may have portions of their armor destroyed). Here's a system (derived from Dark Sun and expanded) for handling partial armor:
Leather armor: A full suit consists of a torso piece and two arm protectors. Having just the torso piece or just both protectors provides AC 1.
Ring/Scale: A full suit of any armor of this level or higher consists of a torso piece, two arm protectors, and two leg protectors. A torso piece provides +1 AC, both arm protectors combined provides +1 AC, and having both leg protectors provides +1 AC.
Chain: A chain torso provides +2 AC, while arm protectors provide +1 AC for both and leg protectors provide +1 AC for both.
Banded Plate/Lamellar: A torso provides +2 AC, each arm provides +1 AC, and leg protectors provide +1 AC for both.
Plate: A torso provides +3 AC, each arm provides +1 AC, and legs provide +1 AC for both
A torso weighs 1/2 the normal weight of a suit of armor, and each arm or leg piece weighs 1/8. The exception is leather, where the two arm pieces each weigh 1/4. For Ring, Scale, and Chain, a single arm and single leg worn at the same time provides +1 AC, the same as wearing two arms or two legs.
Magical piecemeal armor: Each area of the suit (torso, arms, legs) can have a +1 bonus, which is cumulative across different areas, so a full suit of Plate +3 would consist of a Plate Torso +1, Plate Arms +1, and Plate Legs +1. If just the torso piece was worn, it would grant AC 4 (Plate Torso 3, +1 magic). For chain or ring, a single +1 arm can be worn to grant AC 1 (1/2 armor, 1/2 magic), and any magical legs can be worn similarly. Note that Leather armor can only be +2 under this system, since it has no legs.