Digital Integrated Circuits handle discrete signals such as binary values (0 and 1). These circuits use digital logic gates, multiplexers, flip flops etc.  

Analog Integrated Circuits handle contiguous signals. These are two types: linear integrated circuits (Linear ICs) and Radio frequency integrated circuits (RF ICs).

Analog IC design is used in the design of op-amps, linear regulators, phase locked loops, oscillators and active filters. Analog design is more concerned with the physics of the semiconductor devices such as gain, matching, power dissipation, and resistance.

A custom, or full-custom IC, design process uses unique building blocks that are created specifically for the function required. Many of the same tools are used in a custom IC design process that are used in the previously described semi-custom, or ASIC, design process.

Digital IC design is a process of developing a digital Integrated Circuit, this means that the entire IC content is digital. Digital circuits are generally designed from a top-down approach and any digital integrated circuit often has millions of logic cells and connections on one single chip.Analog and digital custom ic design