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### Working with Binary Numbers

Computers are, at the most fundamental level, just a collection of electrical switches. Numbers and characters are represented by the positions of these switches. Because a switch has only two positions, on or off, it uses a binary, or base 2, numbering system (the root bi means “two”). A base 2 system has just two digits: 0 and 1.

Computers usually group these digits into eight place values, known as a byte or an octet. The eight place values are:

27 26 25 24 23 22 21 20

The place values are calculated:

20 = 1

21 = 1 × 2 = 2

22 = 2 × 2 = 4

23 = 4 × 2 = 8

24 = 8 × 2 = 16

25 = 16 × 2 = 32

26 = 32 × 2 = 64

27 = 64 x 2 = 128

So the place values of a binary octet are:

128 64 32 16 8 4 2 1

Thus the binary octet 10010111 can be ...

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