The invention relates to polycarbonate containing a dianhydrohexitol residue, obtainable from a polysaccharide, and a polyol residue, wherein the polycarbonate comprises between 0.2 and 5 mmol hydroxyl groups per gram polymer. The polycarbonate may be branched and comprises functional groups that can react with suitable crosslinkers. The polycarbonate can be used in for example coating compositions.