I'm a Electrical Engineer and this question doesn't make sense to me. Let me start with the basics. Analog circuits use discrete components like Resistors, Capacitors, Inductors, Transistors, Diodes, etc. First of all, all through out school I heard, "Analog is going away, analog is dead". Anyone who says that is a complete idiot. Transistors are inherently analog devices which operate on a convenient digital abstraction to give us the digital functionality we need.
All the traditional RCL (resistor, capacitor, inductor) circuits that are governed by differential equations are analog. ALL real world circuits must use both analog and digital components. The two domains co-exist and you cannot have digital without some analog components.
Your question specifically must be answered in different contexts.
(Sorry if you already know some of this!)
From a signal processing context, a signal is in the digital domain once an analog signal has been sampled (such as voice) into the digital domain through an Analog to Digital converter. Look up a typical DSP (digital signal processing) system flow chart. The signal starts analog, gets sampled into the digital domain, gets processed there and finally gets transformed back to analog so humans can understand it. An excellent example of this is your phone.
From a pure logic and computational point of view: Say you wanted to design a vending machine that gives you your drink and dispenses change. Such a semi-thinking machine can be handled entirely in the digital domain using the concept of state machines, which is simply a mapping of all possible events to states that can be coded and stored in memory. For example a nickel is put in, now the machine waits till a dime is put in... and then when the total money that has been put in equals the cost of the drink, the machine dispenses the beverage. However, even to realize such a circuit on a production circuit board you will still have analog components to provide power or capacitors to clean up the power or perhaps resistors to setup (bias) specific voltages for transistors.
Bottom line is when ANY circuit is actually realized into a circuit board you will have some analog components even if the majority of the circuit is 'deemed' digital. I would actually say all circuits are actually entirely analog but some of the components perform analog functions while others provide digital functionality. The digital domain is simply a convenient binary computational abstraction realized over analog components such as transistors and integrated circuits. Remember, our world is entirely analog: we only see, hear and process in analog not digital. There will always be a need to sample and process analog signals from the real world and ultimately present it back to us in analog.