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Problem 2: Sticks and Stones

Sahil Bhalla and Selim Zoorob

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Prompt

Using Sticks on seesaws to create various logic gates and circuits

0

1

1

0

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OR, AND, XOR, and NOT Gates

How do we make two input gates out of toothpicks on a 2D plane?

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The 10 = 01 Simplification

  • All Gates are Symmetrical (input of 10 = 01)
  • Since this circuit is hand operated we can switch 10 to 01 manually, allowing us to not care about 10 inputs
  • Simplifications
  • A AND B = A
  • A OR B = B
  • A XOR B = (NOT A) AND B

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4-Bit Adder

A Full Adder Adds two bits (plus a carray) and computes the sum and carry out

S = A XOR B XOR Cin

Cout = A AND B OR Cin AND (A XOR B)

4-Bit is just Full Adder 4 Times

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1 Bit Adder and physical design of other logic gates

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Add 0 1

What do we get?

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D = 1

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S = 1

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E = 0

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F = 0

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C out = 0

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Final results:

​

S=1

C = 0 (by default)

C out = 0

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Programming Framework

-Example Calculation through each step of the 4-bit adder

-Gates modelled after toothpick design to simulate

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2x1 MUX and 1 bit adder: Script testing

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2-1 MUX

Chooses Between two inputs based on selector input

Using this formula we can prototype the MUX in code

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2-1 MUX Design

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40cm

40cm

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Input of 0 1 1 in the 2x1 MUX:

​

We obtain 1 (Y=1)

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Conclusions

  • Modern computers are built on simple mathematical concepts
  • Even the most complex algorithms have a relatively simple foundation
  • We barely scratched the surface of binary understanding and its possibilities
  • It is interesting to see that the concepts were translated into a physical device
  • This science has truly paved the our modern future and has changed the understanding of the world around us

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Sources: