Input --> A, B
Output --> S (Sum), C (Carry)
Adds two binary bits together, the output gives a sum and a carry bit (if both bits are 1).
Input --> X, Y, C-in (Carry In)
Output --> S (Sum), C-out (Carry Out)
Adds three binary bits together, the output is a sum and carry. A full adder is two half adders combined together.
Stringing ful adders together makes CPUs.
This special circuit is used to hold a value temporarily. These consist of 2 NOR Gates whose outputs are one of the inputs of each-other. To its design, the circuit can only retain a 1 bit value as the power is provided, meaning that conversely, once the power is lost, so is the bit.
We call this Volatile memory, and a common examples are Computer RAM that enable the CPU to store data temporarily to reduce load and make fetching faster. These circuits can be arranged in 8bits of data, or 16, 32 to 64 bits (multiples of 8 bits is the standard).