Homework 1
1. We have a number system of ten mainly because people count by putting the same amount of things on the ground, like branches or stones. Then, they started to use fingers instead because it is easy to carry with. When people found that they can't count when both hands are full, which means ten, they have nothing to do with it. After great invention of zero, they are able to express all kinds of numbers, but they still count them ten by ten according to their habit.
2. On the base of ten, each digit represents a power of ten. 465, for example, is total of 4 times 10 to the 2 power, 6 times 10 to the 1 power and 5 times 10 to the 0 power. It is the same on the base of two, so in binary, 11011011 is the addition of 2 to the 7,6,4,3,1,0 power. The result is 219.