HALF ADDER:

Gates: XNOR, IMPLIES

Torches: 12

Redstone: 7

Blocks: 19

Size: 5X4X4

This adder will take 2 bits and add them together. The resulting bit will be the output of S (sum). If both bits are 1, there will be a carry over, and C will become 1 (C will become 0). This half adder can be modified to create a non inverted C output, but this configuration is used so that it can be implemented as the start of a chain of full adders.

(EXTENSION): for those new to advanced redstone like myself, it's eaiser to understand it like this: let's say output B (C) has a NOT gate that inverts the signal and it leads to an iron door or piston door etc. output A (S) is connected to sticky pistons controlling the floor. let's say for sake of argument that there is 1x1x1 block NOT affected by the sticky pistons, this is the Safety Block. when you activate input A, both the door will open and the floor will drop, if you're standing on the Safety Block, then you will not fall. input B will control only the floor, but if input A is on the input B will control them both. when both are on, input A will only affect the floor. this means if you are off the server and want no one in, leave A and B on, when they deactivate A, the floor will drop, but the door will stay closed, so if they know the secret, they still can't get in.