Routing TCP/IP, Volume I (CCIE Professional Development)

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 ...