The ASIC (Application Specific Integrated Circuit) was the equivalent of the ULA (Uncommited Logic Array) in the ZX Spectrum, a multi-purpose logic chip to provide functions that would normally require discrete logic chips and hence extra cost.
The ASIC was also responsible for some Hardware Bugs and limitations due to the amount of available pins on the package.
Originally the SAM ASIC was to be produced by Fujitsu in a 68 pin package. Moving to VLSI and an ASIC design with 84 pins allowed for improvements, such as an increase in the number of colours.
According to Dave Park there are two different types of ASIC, the earlier 1989 run and the later 1990 run, the latter being a different fabrication process that meant they ran much hotter in operation, up to 60 degrees celsius.