Pulley Logic Gates

spring-of-mathematics:

By 

Alex Gorischek

To demonstrate how computers work, he has made a physical example of how binary logic gates work using pulleys and weights. For anyone who doesn’t know much about logic gates (Wikipedia), it’s a great lesson in one of the fundamentals of circuitry. Using an old chessboard, eyelets, rings, weights, and string, Alex has designed a system that can show off all of the logic gates. This includes: NOT, BUFFER, NAND, AND, OR, NOR, XOR, XNOR. 

Not

0 in, 1 out; 1 in, 0 out.  Whatever you put in, you don't get out.

( GIFs: via Imgur – From: https://vimeo.com/93042377 by Alex Gorischek  )

image

Buffer

If you take the not of not, you get what you put in – 0 in, 0 out, 1 in, 1 out.

image

Nand

Both inputs must be brought up to 1 to lower the output to 0.

image

And

If you negate the result of Nand, you get And.  Both inputs must be brought up to 1 to raise the output up to 1.

image

Or

If you not both inputs, and then Nand them together, you get Or.  If either input is raised to 1, the output raises to 1.

image

Nor

Negate both inputs, nand them together, and negate the output.

image

Xor

Xor is complicated – The large weight ands the inputs together.  The medium weights negate the inputs, but are pulled up by the large one when both are 1.  When you nor those together, you get Xor.

image

Xnor

This is comparatively simple – just negate the output of Xor, and you&

#039;re there!

Source:

image

The principles of logic can be realized in so many systems that it makes you understand how they really are universal. All you need is something that takes an input and produces the opposite output – a NOT gate; something that take two inputs and produces an output when any one of the inputs is active – an OR gate; and something that takes two inputs and produces an output only when both inputs are active – an AND gate. Once you have AND, OR and NOT you can build any other logic gate you need. They form a universal basis for logic. You can even do better – a single NAND, i.e. a NOT AND gate, is universal. Yes, you can make any other logic gate by simply combining NAND gates.

This sounds powerful but you also need to keep in mind that you can use logic gates to build a fully functioning computer. All you need to build a computer is lots of NAND gate.

Pulley Logic Gates demonstrates how a set of ropes and pulleys can be used to implement the basic gates. To understand what is going on notice that binary values correspond to zero or one as written on the board – i.e. up is 1 and down is 0. For example, you immediately get a NOT gate with a single piece of rope. When one end is up the other is down and vice versa – it is an inverter.

image
image
image
image

Leave a comment