In the last post we discussed how to make basic gates in Minecraft using redstone. This post will match up with Chapter 12, in which we’ll build a full adder out of two half adders.
The half adder
This looks complicated initially, but it’s very simple and easily translates from
any half adder circuit diagram. A half adder takes two inputs. It
inputs to generate a sum bit (S) and
ANDs the inputs to generate a carry bit
Our two inputs are on the left side (the levers). They branch upwards into
AND gate immediately, which results in C. Therefore the rest of the
circuit must be the XOR gate. XOR gates are a little complicated, they are
made out of
ANDof the results of 1 and 2
We can see in the middle of the circuit is our
OR gate for the
On the very bottom of the circuit, we have a familiar and gate. Notice that
at the very bottom right corner, there are two inverters in series. The first
inverter in that series is the last component required to complete the
The second inverter turns the
AND into a
Finally the results of the
OR and the
NAND are fed into another
Both of the wires then proceed to the top center where we have two redstone lamps. The lamp on the left is the carry bit C. The lamp on the right is the sum bit S.
If you are following along (or better yet building along!) take a moment to convince yourself that this does implement half addition correctly. It may help to draw a truth table for one or more sub components.
The full adder
This circuit includes the half adder from before and another half adder. The redstone
lamp near the middle of the circuit is the carry bit C from our first half adder.
The wire running near the bottom middle is the sum bit from the first half adder.
These two signals swamp places in the center of the circuit with the carry bit
running down to be
ORd with the carry bit from half adder #2 and the sum bit from
the half adder #1 being used as the input signal to half adder #2.
Knowing that, we can follow the components of the second half adder the same way we followed the components of the first half adder. The output of the carry bits correspond to the left redstone lamp on the bottom of this circuit. The final sum bit corresponds to the right redstone lamp.
This particular design of circuit is extremely difficult to extend for two reasons
- The size of the gates. Our AND gate for instance takes up several blocks. We would need a much more compact AND gate design in order to make planning the circuits easier.
- We cannot easily clone components (like gates) and think at higher layers of abstraction. This also makes building a reliable circuit difficult since it’s very easy to screw up an AND gate very deep in a circuit.
Chapter 13 discusses subtraction which I will not be building a circuit for. Chapter 14 discusses memory, so we’ll get to see how to build a simple circuit which can hold a value.