Feature

# 3D Printed 10-bit Binary to Decimal Converter

Matheus Postigo

Issue 60, July 2022

An easy to use 3D printed tool to convert binary to decimal and vice versa.

We just love seeing practical 3D printed tools to help solve real-world problems. In this case, it’s a simple 3D printed aid to help you convert binary to decimal or decimal to binary. All, by simply flipping small plates with your fingers, then looking a the results to get your answer.

We caught up with the designer to find out more.

An easy to use 3D printed tool to convert binary to decimal and vice versa.

My name is Matheus Postigo, a Chemistry Professor at UTFPR (Federal Technological University of Paraná), in Brasil's south region. Besides loving Chemistry, I'm also into music, gardening, photography, astronomy and more recently into 3D modeling and printing. Even though I'm a junior level maker, I already made some useful tools and objects. I think 3D Printing is a very useful tool to master.

Yes. 3D printing is not just about printing fancy artwork. What was the motivation for designing your Binary to Decimal model?

Even though there are similar models available online, I thought making my own would be a nice challenge. Also, I only found some print-in-place models and with a lower number of bits. So I designed a simpler version that you can assemble later, for easier printing. Finally, I'm interested in any kind of educational tool, and this converter can be a nice one for teaching binary logic.

How does it work, and for our readers not familiar with Binary, can you summarise the concept?

Unlike the decimal system, which has 10 digits for counting, the binary system relies only on 0 and 1. This can be a limitation, but also an advantage, since 0 and 1 can be translated electronically as ON and OFF or YES or NO. This way, many complex mathematical operations can be done by a simple circuit.

Here are a few examples of how it works.

# To convert from binary to decimal

Build the binary number on the top part, lifting the plates when you need a 1 and lowering them when you need a 0. Always align the number to the right, following the logic of a calculator.

Sum all the powers of 2 that are uncovered by plates to get the decimal number.

# Example 1:

## Convert 101110 to decimal.

1. Build the number, aligning to the right. The top part will read: 0000101110.
2. The covered powers of 2 will be: 512, 256, 128, 64, 16 and 1.
3. The uncovered powers: 32, 8, 4 and 2.
4. Adding up these numbers we have: 32+8+4+2 = 46

## Convert from decimal to binary:

Factorate the decimal number in powers of 2, and uncover these numbers, which will lead to 1s on the top part. Cover the powers you don't need, which will lead to 0s. Read the binary number above.

# Example 2:

## Convert 733 to binary.

1. Factorate 733 to powers of 2, which will lead to the following sum: 512+128+64+16+8+4+1.
2. Note that the powers 256, 32 and 2 are not used, so they should remain covered.
3. The resulting binary number reads: 1011011101

Very neat. We imagine young students could benefit from this also. We notice you updated the design recently on your Thingiverse. What is the difference between this and your first design?

The only update was to narrow the holes in the model for the shaft. The first design was supposed to need a metal rod (brass, copper, steel, etc.) to serve as a shaft for holding the plates and allowing them to turn. But one day I realized that such a specific rod can be hard to find, and if there's something readily available for any 3D maker is printing filament.

So I made the holes smaller for the standard 1.75 mm filament. All you need to do is to straighten a piece of it with a heat gun or boiling water and use it as a shaft, making sure to melt the ends to avoid it falling off.

Using a length of filament is a brilliant idea. If our readers are inspired to make one for themselves, is there anything they should know before printing and assembling?

Just print it with a nice resolution (0.2 mm should be fine) and slowly, so the details are preserved. For the plates, print them sideways, so their sides face the printing bed. This way the plates print faster and stronger. I recommend using a little brim for them, so they don't detach from the bed during printing. The assembling is pretty straight forward, just put the plates with the 1s facing up over the 0s and pass the shaft through all the holes, locking the ends by melting them. I like to print it in two different colours but that's completely optional.

Great. We hope our readers can print their own and put it to good use. What are you working on next?

I'm always working on different projects, it's so much fun. I'm experimenting with ukuleles, flutes, bird feeders, a DNA/RNA educational model, a chemistry model for molecule assembling for the visually impaired, and more recently, two different colorimeter chambers for chemical analysis using a smartphone camera.

Wow. Sounds like you don’t sleep. Perhaps we can look at featuring more of your projects in the near future. Thanks again for your time.