I was looking for a very simple explaination of binary numbers and found this great math website for kids calleded, Ducksters. This is how they explain binary numbers: 

The binary number system is a base-2 number system. This means it only has two numbers: 0 and 1. The number system that we normally use is the decimal number system. It has 10 numbers: 0-9.

Binary numbers are very useful in electronics and computer systems. Digital electronics can easily work with a sort of “on” or “off” system where “on” is a 1 and “off” is a zero. Often times the 1 is a “high” voltage, while the 0 is a “low” voltage or ground.

How do binary numbers work? Binary numbers only use the numbers 1 and 0. In a binary number each “place” represents a power of 2. For example: 1 = 20 = 1 10 = 21 = 2 100 = 22 = 4 1000 = 23 = 8 10000 = 24 = 16 Read more at: http://www.ducksters.com/kidsmath/binary_numbers_basics.php

Second grade students will explore the world of base-2 using a unique challenge called “Exploding Dots”, which was created by James Tanton. 

Watch the videos below to get an overview of this challenge.