# One Hundred Cheerios in Binary

My son had to do a project for his 100th day of first grade. Since I’ve been teaching him binary — he knows the powers of two from 1 to 512 — we decided to incorporate it into his project. His assignment was to assemble 100 objects in a creative way. This is as creative as I get:

The places in binary represent powers of two, analogous to how the places in decimal represent powers of ten. To convert the binary number 1100100 to decimal, just add the columns that have a 1 in them: 4 + 32 + 64 = 100.

There are 100 Cheerios; the 1s have eight Cheerios each, and the 0s have 19 each.

For those students (and teachers) that will be seeing binary for the first time, I wonder how confusing it will be that the decimal equivalent of 1100100, that is, 100, has just 1s and 0s in it! And will they wonder if the two sub strings of ‘100’ in the binary number have any significance? (Actually, since 100 is a power of 10, the trailing ‘100’ is not a coincidence.)

(His 100-day Kindergarten project also had a binary theme, but I don’t seem to have a picture of that one. It was three towers of pennies glued to poster board: one of 64 pennies, one of 32 pennies, and one of 4 pennies. If I recall correctly, the dimensions (width x height) were 4×16, 4×8, and 1×4.)