### Mechanical computation from Lego bricks

Coming home from college allows me to see some of the things I hold dearest to my heart: namely, my Legos. While still at school, I stumbled across Martin Howard’s Lego logic gates and made a mental note to try building my own when I got home. However, Martin’s Lego logic required a lot of gears and rack-and-pinion pieces that I don’t have a lot of. I set about building my own renditions of logic gates out of Legos, looking for a design that is smaller, uses less specialized bricks, and can be used to build larger mechanical circuits.

**For the non-computer-scientists**

All computers are based on the fundamental principle of transistor logic – that is, that all computation in a computer is done by large combinations of on-and-off switches, wired together in meaningful ways. Transistors are used to create “logic gates”, which are the fundamental building blocks of everything in a computer. This isn’t limited to just desktop computers – phones, iPods, and even those cheap electronic pocket games from McDonald’s happy meals, are all based on transistor logic. In conventional digital circuits, the basic gates take inputs in the form of an electrical current running through a wire (represented by a ‘1’ in Boolean logic), or the lack of one (represented as ‘0’), and produce an output based on the input. Put simply, a logic gate is like a yes/no question – two wires are connected to a logic gate, carrying either a high or low current, and the logic gate outputs a high or low current onto a third wire based on the combination of currents in the two wires.

For example, an AND gate outputs a 1 only if both its inputs are 1, and 0 otherwise. The OR gate outputs a 1 if either of its input wires carries a current, the XOR outputs a 1 if only 1 of its inputs is 1, and so on. In computers, these gates are combined to form bigger logic functions – addition, subtraction, and any other mathematical operation can be performed using logic gates. In the combination of gates, the output of two separate gates will be the input of another, which combines with other combinations of gates to be inputs to other gates, and so on.

For my Lego logic gates, current traveling through a wire is replaced by a horizontally-moving axle. The axle pushed forward represents a logic ‘1’, while the axle backwards represents a logic ‘0’. The position of the axles determines the position of a third axle moving out of the gate, which is then used as input to further gates. For the rest of this post, a ‘1’ represents an inward moving axle, and a ‘0’ for the converse.

**The NOT gate**

I decided I’d start with the easiest gate – the NOT gate. This was made by having the axle push a lever around a central axis at one of its ends, and connect the other end to the output axle.

To maximize space, I stuffed two NOT gates into one enclosure. It was tricky trying to minimize the amount of room the lever took, but after playing around with several designs, I finally settled on the one above.

**The NOR gate**

Since all of the basic logic gates can be built out of combination of NOR gates, I decided I would take on this one next. It turned out to be surprisingly easy – just a wider modification of the NOT gate.

One of the most troublesome aspects of building these gates was making sure that the amount of axle motion is uniform- that is, an axle moving a certain distance into the gate should move the output axle by the same distance.

**The AND gate**

The AND gate can be built by inverting the inputs to a NOR gate. It was made by simply combining the 2 NOT gates and the NOR gate above.

This gate was the first gate built from the combination of smaller gates. If computer scientists cared about naming conventions as much as biologists do, I assume this would be called a “polygate”.

This front view shows the AND gate with both its inputs as ‘1’.

**The XOR gate**

An XOR gate is crucial for building ALU’s (arithmetic logic units), especially ones that can add and subtract. The XOR had to be built by first converting an XOR gate to NOR logic, then building the individual components and hooking them together. This ended up as an addition of two gates to the AND gate.

The XOR gate above uses 3 NOR gates and 2 NOT’s. Here’s a more detailed schematic.

**Combining the gates**

As demonstrated by the XOR gate above, more complex logic is relatively easy to build out of less complex building blocks. I’m currently working on combining the gates into a full adder, which can be combined to form an ALU (arithmetic logic unit). If I’m still feeling adventurous after that, I may try building all the other elements of a computer as well – decoders, switches, flip-flops, and the rest of the digital circuit family. And if I manage to find some serious motivation (and some elves to help me assemble Lego logic gates), I may someday write a post about the world’s first Lego computer.

This is so fucking cool. Finally took the time to completely read it. I LOL’d at “and some elves to help me assemble Lego logic gates”. That’s what outsourcing is for. ;-)

Wow, your gates are small! I am slightly puzzled with regards to one aspect of their operation though. How does the NOR gate give an output of 1 with inputs of 0,0? The input axles look detached from the central mechanism …

I find your logic gates outstanding! The Flip-Flop might prove tricky though. I’d be very interesting in seeing if you manage to build it!!

I’m also interested in mechanical computation, and have done my own experiments. check out my LEGO logic gates here: https://sites.google.com/site/santiagoontanonvillar/Home/lego-projects/konrad-zuse-s-logic-gates

I also built a simple finite state machine using those gates. Here: https://sites.google.com/site/santiagoontanonvillar/Home/lego-projects/finite-state-machine

Keep us posted in your attempts of building the first LEGO computer! This is an exciting project!

[...] Saharia blog post Mechanical computation from Lego bricks was interesting, but I was not quite satisfied with his NOR gate. First of all the OR gate in it [...]

Reference in an answer on a Stack Exchange site. http://bricks.stackexchange.com/a/112/178

this is soooo cool. can some one tel me where i can buy a lego set for this ( online )