One Hundred Acorns in Binary

Today is the 100th day of school at my son’s elementary school. I’ve had my binary influence on prior 100th day projects, and this year was to be no different. But alas, his class is not doing one this year. I didn’t want to waste the acorn tops we saved though, so I made my own 100th day project (well not quite — I didn’t glue them):

A Binary Multiplication Problem Expressed With One Hundred Acorn Tops
A Binary Multiplication Problem Expressed With One Hundred Acorn Tops.

(Notice it’s a little asymmetric. The zero in the upper right has only 15 acorn tops, not 16 like the rest; I stole one for the times sign.)

There are two ways to solve this problem. The first way is to convert the operands to decimal and then multiply using decimal arithmetic:

  1. Binary 1010 = 1 x 23 + 0 x 22 + 1 x 21 + 0 x 20 = 23 + 21 = 8 + 2 = 10 decimal.
  2. 10 x 10 = 100.

The second way is to multiply using binary arithmetic and then convert the answer to decimal:

  1.       1010
        x 1010
        ------
          0000
         10100
        000000
       1010000
       -------
       1100100
    
  2. Binary 1100100 = 1 x 26 + 1 x 25 + 0 x 24 + 0 x 23 + 1 x 22 + 0 x 21 + 0 x 20 = 26 + 25 + 22 = 64 + 32 + 4 = 100 decimal.

The first way is easier, but it’s not as much fun 🙂 .

Dingbat
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