IP Addresses are stored as binary numbers in four 8-bit bytes (strings of 0\'s a

Question

IP Addresses are stored as binary numbers in four 8-bit bytes (strings of 0's and 1's). For ease of reading, these are translated into their four equivalent decimal numbers, separated by dots, to form "dot separated decimals." Use the facts given about binary numbers, along with the multiplication principle, to answer the following questions about IP addresses: a. What is the decimal value of the binary number 10101011? b. How many different decimal values are possible for an 8-bit binary number? c. How many different IP addresses can be stored as described above?

Explanation / Answer

a. The decimal value of 101010112 is 20 * 1 + 21 * 1 + 22 * 0 + 23 * 1 + 24 * 0 + 25 * 1 + 26 * 0 + 27 * 1 = 1 + 2 + 8 + 32 + 128 = 171.

b. The number of different decimal values possible with 8 bit binary number is: 256. Starting with 010 (000000002), and will end at 25510 (111111112).

c. The number of different IP addresses that can be stored is: 0.0.0.0 (ofcourse this is not a valid IP), to 255.255.255.255. Therefore, the total number of different IPs are: 2564 = 4,294,967,296.

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