What is binary?
Binary, or "base 2," is a numbering scheme in which each digit is either 1 or 0. Unlike in the "base 10" numbering scheme that we are familiar with, the weight of the digits increases by a power of 2. Each digit is multiplied by the power of 2 of its digit place and then summed to compute the total value of a number.
What are logic gates?
Logic gates perform logical operations on binary inputs. Common boolean operations include “AND,” “XOR,” and “NOT.” “AND” outputs 1 if both inputs are 1. “XOR” outputs 1 if one input is 1 and the other is 0. “NOT” inverts the input, changing a 0 to a 1 and a 1 to a 0. Typically, logic gates are built for computers with diodes and transistors, and they can be combined to compute more complicated binary operations.
What is abstraction?
In computer science, abstraction is the act of representing essential features without including the specific details of how they work on the inside. If we have logic gates that we know will output a certain value, we can build larger calculators and computers without knowing the background of how each individual gate works. Sometimes, this is referred to as a "black box" system.
Mechanical Analogy
Usually, logic gates use current going through transistors and diodes. However, we can build logic gates that use falling marbles instead of electrical signals. In this case, a marble represents a 1 while the absence of a marble represents a 0. We can combine logic gates to compute mathematical operations. This mechanical analogy demonstrates how a seemingly complex system like a computer can be decomposed into multiple smaller, understandable chunks, demystifying the behind-the-scenes “magic” going on inside a computer. The final product is interactive and visually stimulating. It can be used to learn about binary, logic gates, debugging, clocks, Moore's law, and abstraction.
Mechanical Logic Gates
We designed the gates using AutoCAD and then cut them out of ¼ inch plywood with the laser cutter. We glued together two layers of ¼ inch plywood to create ½ inch channels for the marbles to pass through. The gates are placed on frames with detailed information at 20 degree angles. We use the same AutoCAD gate designs while building the full adder.
Mechanical Full Adder
Using the gravity-controlled logic gates that we designed, we put together the “Full Adder,” a fundamental building block for building large-scale computation machines. Can you spot which logic gates we used in the Full Adder and where they are? The full adder computes the sum of two 1-bit inputs. With multiple Full Adders, we can extend the single-bit calculator to any number of bits. A modern computer often uses a 64 bit computer architecture. This highlights the importance of creating tiny transistors — if transistors were the size of our Full Adder, computers would have to be huge!
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