Embedded system
If the device needs to be very small or will be sold in very big numbers ("high-volume"), it makes sense to make a custom or specialized chip that does exactly what is needed.  This is a system on a chip (SoC) which holds a complete system - processor, floating point unit, memory cache and interfaces on a single integrated circuit. SoCs can be made as a special-order application-specific integrated circuit (ASIC) or by using a field-programmable gate array (FPGA) which is programmed by the people building the embedded system.