Why all Digital Electronics Circuits use DC and Not AC?

The question will be little confusing.
But the answer is simple.

AC Vs DC

In Digital Electronics, Gates are the basic Elements.
Actually this Gates are made up of Transistors.

NAND gate using Transistors

Transistors are working as a Switch in Digital Electronics.

Transistor as a Switch

ie, When control signal is present, Transistor is ON, otherwise Transistor is OFF.

Now, What is this Control Signal?

That is the Signal Applied to the Base of the Transistor.

The Switch must be ON till the control signal is present and the Switch must be OFF till the control signal is absent. 

Switch with Control Terminal

Now consider applying AC signal as the control signal to the Base of the Transistor.

The AC signal will vary from Positive peak to Negative peak going through the 0V.

So how can we keep the Transistor ON and OFF as per our requirement?
It is not possible.

Now consider DC. It is Direct current and it is constant in value.
So if we apply DC to the Base of the Transistor as a control signal, we can keep the Transistor ON of OFF as per our wish.

That is In digital Electronics, We need only HIGH signal and LOW signal, not the intermediate values. 
Hence we cannot use AC in Digital.

Now consider Transistor working as an AMPLIFIER.
Here also, the transistor is working in DC (Power supply of the Transistor is DC), but the input is an AC signal.

Transistor as an Amplifier

Thus Amplification of AC signal is just an application of the Transistor and that doesn't mean that the Transistor is working in AC.

Why cant we power the Transistor with AC?
We can apply AC as a Power supply to the Transistor.
But the transistor will not give the desired operation.

Biasing of Transistor (a) NPN  (b) PNP

Because, for acting as a Switch or Amplifier, the transistor should be biased.
In order to keep the transistor in constant Biasing conditions, we need Constant current. ie DC.

If we apply AC as a power supply to the transistor, the Biasing conditions of the Transistor will be varying in each cycle of the AC signal.

Hence the transistor will not work properly.
This is the reason why we convert the AC signals into DC using Rectifiers in the Power supply section of the Electronic Devices.

(We can apply the same principle to MOSFET also.
MOSFET are used as switches in Digital Electronics as Switches.
Working principle of MOSFET is same as that of the Transistor.
However, MOSFET is a Voltage controlled Device, but Transistor is a Current controlled Device.)

Logic Signals

  There are a number of different systems for representing binary information in physical systems.  Here are a few.

• A voltage signal with zero (0) corresponding to 0 volts and one (1) corresponding to five or three volts.
• A sinusoidal signal with zero corresponding to some frequency, and one corresponding to some other frequency.
• A current signal with zero corresponding to 4 milliamps and one corresponding to 20 milliamps.
• And one last way is to use switches, OPEN for "0" and CLOSED for "1".
• (And there are more ways!)

Advantages of DC over AC

However there are some advantages for DC over AC

DC power maintains a constant direction of current. One advantage of DC power is there is no reactance in the line. 

This allows higher power transfer capability, higher capacity utilization of generators, and less of a voltage drop along the line. 

DC also has a lower line resistance than AC because of the “skin effect” in AC. This is when charge is carried mostly near the outside of the wire.

In the DC system, power is just the real component. This means that the transmission system operator need not worry about the sufficiency of reactive power to maintain the security and stability of the system.

In DC, there is no frequency, so generators connected to the transmission grid do not need to be synchronized.

The DC system does not introduce susceptance along the line thus removing the effect of changing current and over voltages in the system.

Analysis of DC systems only involves real numbers, while AC systems involve complex numbers. (Think about a world without AC; How easy will be the calculations in Electrical Engineering :-) )