7.3 Representation of IP and MAC addresses
This part explains how the binary numbers of an IP address and a MAC address are represented to be more readable for humans. There are two videos in this part – each video is followed by an activity.
Watch the video below, which is about 4 minutes long.
Note that at 00:45 the speaker says ‘provides nearly 4 million 3 hundred different addresses’, but meant to say ‘provides nearly 4.3 billion addresses’.
Activity 5 Test yourself
What is the highest decimal number that could be represented by 10 binary symbols? (Hint: use the formula introduced in the video.)
The formula is 2n − 1. You need to substitute a 10 for the n in the exponent. This gives 210 − 1 = 1024 − 1 = 1023.
Watch the video below, which is about 3 minutes long.
Activity 6 Test yourself
1. What is the decimal equivalent of hexadecimal D?
D is the hexadecimal equivalent of decimal 13.
2. Use the Windows calculator or an online converter to ascertain the highest possible MAC address. (Hint: it’s easier to enter this in hexadecimal rather than 48 binary bits.)
You know that 48 binary bits of a MAC address are represented by 6 pairs of hexadecimal numbers. The highest hexadecimal number is F so you will need to enter F twelve times: FF FF FF FF FF FF. This will produce the decimal equivalent 281,474,976,710,655.
3. If instead the highest MAC address was represented in dotted decimal, what would it be? (Hint: the highest MAC address in binary has a 1 in every place.)
The highest binary number for any given number of bits would have a 1 in every place. 48 bits would be 6 octets and the highest decimal number that can be represented by a binary octet is 255. Therefore, if this were to be represented in dotted decimal it would be 255.255.255.255.255.255.
Note: in many other contexts 8 bits are referred to as a byte, but in the context of MAC addressing it is more normal to refer to 8 bits as an octet.