Full Adder:
A full adder is a combinational logic circuit that adds three binary digits and produces a sum and a carry output. It is an essential component in arithmetic circuits, such as arithmetic logic units (ALUs) and microprocessors.

Inputs and Outputs:
A full adder has three inputs - two binary numbers (A and B) to be added and a carry-in (Cin) from the previous stage. It has two outputs - a sum (S) and a carry-out (Cout). The sum output represents the least significant bit (LSB) of the addition result, while the carry-out represents the most significant bit (MSB) or the carry-over.

Binary Digit Inputs:
The question states that a full adder has three binary digit inputs. This means that each input can take on one of two values - 0 or 1. The two binary numbers (A and B) represent the bits to be added, and the carry-in (Cin) represents the carry-over from the previous stage.

Binary Digit Outputs:
The full adder has two binary digit outputs. The sum output (S) represents the bit that results from adding the two input bits and the carry-in. The carry-out (Cout) represents the bit that is carried over to the next stage of the addition.

Explanation of Option B:
Option B states that a full adder has three binary digit inputs and two binary digit outputs, which aligns with the definition and operation of a full adder. The three inputs (A, B, and Cin) are binary digits, and the two outputs (S and Cout) are also binary digits.

Other Options:
Option A states that a full adder has two binary number inputs and two outputs, which is incorrect. A full adder requires three inputs - two binary digits and a carry-in. Option C states that a full adder has three binary digit inputs and three binary digit outputs, which is also incorrect. A full adder has two outputs - a sum and a carry-out. Option D mentions NAND and OR gates, which are components used to implement the logic of a full adder, but it does not accurately describe the inputs and outputs of a full adder.

Therefore, the correct answer is option B - a full adder has three binary digit inputs and two binary digit outputs.