My name: Mary-Anne

Question Level: elementary (K-5) 2nd grade
Who is asking question: other (parent with a degree in math!)

My second-grade son brought home a fun math worksheet which involved calculating sums using "Papy's Computer." I had never heard of this before and found it to be quite interesting. Each digit in a decimal number is represented by a 2x2 grid. Each grid square corresponds to one of the numbers 1,2,4, or 8.

Have you heard of "Papy's Computer"? Is it based on some math theory? Does it have any real-world applications?

Thanks for your help.

Mary-Anne

Hi Mary-Anne,

The technique behind this "computer" has significant real-world applications but this is a bizarre way to present it. The technique is "base 2 arithmetic", which is the way that computers do arithmetic. Notice that 8 = 23, 4 = 22, 2 = 21 and 1 = 20.

I want to think of the entire number, not its digits, and write the "grid" as a 1x4 grid rather than 2x2. Reading from left to right the positions are the 23 (8) position, the 22 (4) position, the 2 position and the units position.

In this grid you can write the integers from 0 to 15. For example 10 is 8 + 2 so 10 is represented by

 1 0 1 0
Likewise 3 is 2 + 1 so 3 is represented by

 0 0 1 1
Adding these as I am sure you son was shown how to add using the 2x2 grid gives

 1 1 0 1
which is 1x8 + 1x4 + 0x2 + 1x1 = 13. This "base 2" notation is more usually written 11012. Thus

10102 + 00112 = 11012

Using a 1x4 grid allows for expansion. If you want to represent a number larger than 15, say 22, expand the grid to 1x5 with the new position the 24 (16) position. Thus

22 = 101102

Another base 2 activity (trick?) you might find interesting is in a note written by Penny called What's my number? If you print the first page, cut out the six cards (or maybe just use the first 5) and teach your son how to use them it will give him some arithmetic practice with a fun activity.

Harley
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