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Binary Numbers 101

For this exercise, we are looking at representing positive numbers and 0 (also known as "non-negative numbers") in binary.

• Fill in the table below:

  Number of bits	Values we can represent	How many are there?	Maximum value
  1	0, 1	2	1
  2	00, 01, 10, 11	4	11, aka 3 in decimal
  3	000, 001, 010, 011, 100, 101, 110, 111		111, aka ? in decimal
  4			1111, aka ? in decimal
  5			11111, aka ? in decimal
  6			111111, aka ? in decimal

• What is the relationship between the number of values we can represent with N bits and the maximum value we can represent with N bits (assuming we are only representing positive numbers and 0)?
   
• Run your Powers of 2 program. What connection do you see?
   
• How many numbers can we represent with N bits? What is the maximum value (assuming we are only representing positive numbers and 0)?
   

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