BROCADE IP PRIMER

Chapter 2: TCP/IPWhat we're talking about is binary. Binary is a way to represent numbers. It'slike decimal, but in decimal, we have ten digits. In binary, we have two. In decimal,you would count 0,1,2,3,4,5,6,7,8,9,10. In binary, you would count0,1,10. That last number looks like a number ten, doesn't it? It's not. If you'reusing binary, that number represents the number two.In decimal, each digit place represents a multiple of ten. For example, 10, 100,and 1000 represent ten (10 x 1), one hundred (10 x 10), and one thousand(10 x 10 x 10). If we see “10,000,” we know that as ten thousand (10 x 10 x 10x 10), because there's a “1” followed by four zeros. Binary works in a similarfashion, but instead of multiples of 10, it's multiples of two. For example, 10,100, and 1000 in binary represent two (2 x 1), four (2 x 2), and eight (2 x 2 x2). And if we were to take it one step further, “10000” would represent sixteen(2 x 2 x 2 x 2). As decimal is referred to as base 10, binary is referred to asbase 2.128 64 32 16 8 4 2 10 0 0 0 0 0 0 1Why am I telling you all of this? You'll find out very quickly. As I mentioned inthe previous chapter, switches and routers are computers. They have a CPU.They have RAM. As such, they also operate in binary.You would do very well to memorize the diagram on this page. It will help you inmore ways than just impressing your friends.The first example of using binary is in the IP address itself. I gave you an exampleof an IP address: 192.168.100.1. There are four decimal numbersseparated by a period. But what you need to know is that the computers,switches, and routers see that number this way:1100 0000 . 1010 1000 . 0110 0100 . 0000 0001Notice that each of the four decimal numbers are represented by eight binarydigits. You usually call a binary digit a bit. So, each of the four decimal numbersare represented by eight bits. Let's look at the first number: 1100 0000.You've got a 1 in the 128 bit place, and a 1 in the 64 bit place, and all the restare zeros. So, if you add 128 + 64, you'll see that you get the number 192.Likewise, the next number: 1010 1000. Here, we've got a 1 in the 128 bitplace, a 1 in the 32 bit place, and a 1 in the 8 bit place. This number, in decimal,would be 128 + 32 + 8, or 168. The third number is 0110 0100. This hasa 1 in the 64 bit place, a 1 in the 32 bit place, and a 1 in the 4 bit place. Thenumber is 64 + 32 + 4, which equals 100. And the last number's the easiest.You've only got one “1,” and it's in the 1 bit place. The binary number “00000001” equals our decimal “1.”Let's look at eight bits. To get the smallest possible number (with just eightbits), we could set all of the bits to 0, right? This would give us the number 0.To get the largest possible number, we could set all of the bits to 1. This wouldgive us the number 255 (128 + 64 + 32 + 16 + 8 + 4 + 2 + 1).40 Brocade IP Primer