A full adder is comprised of 2 half adders and an OR gate. Ours is specially designed so that carry-in and carry-out are at the same height. This allows multiple full adders to be linked together.
The full adder is on the right. The handsome man on the left is Jeff. This photo was taken in the Academic Center at Olin.
| This test shows what happens when the inputs are A=1, B=0 and Carry In=1. 1+0+1 = 10 which is a carry and no sum. | |
A half adder takes two, 1-bit inputs and outputs their sum as one, 2-bit value. It is made up of an AND gate and an XOR gate.
Since it has the same number of inputs as outputs, it is easy to create a version using balls. We use a stated XOR to compute the digit in the one's place, and a waiting AND to compute the amount that carries over into the two's place. The A ball goes in and becomes the CARRY, while the B ball becomes the SUM.
This photo of our K'NEX half adder is from the XOR gate side.
| The position of the ball represents binary state. Left is 1; right is 0. Inputs: A is in the back; B is in the front. Outputs: Sum is in the front; Carry is in the back | |
The OR Gate
This gate takes two balls A and B as inputs. It outputs A and (A || B).
The AND gate is a mirror image of the OR gate.
We are building a computer out of KNEX. So far we have made a 1 bit full adder, memory, and decoders. You can view our progress through the following posts on this blog. You can also watch videos of the various parts in action on Google Video. Just search for KNEX computer.
