Subnetting Demystified - Part 3 Binary Math

This video presentation contains a review of IP addresses and the layers of the OSI model as they relate to IP addressing and routing.

UPDATE 11/3/15

First, thanks to all who have viewed our Subnetting Demystified videos! Based on comments we have received, there seems to be some confusion regarding the information shown on the whiteboard at about 7:44. We have added two annotations to the video that will hopefully clear up the confusion. I’ll also provide some additional information here.

In the video (again, at 7:44) I have shown on the whiteboard an eight-digit binary number and above each binary digit, I have written the bit-weight for each position. Above, that, I have written the powers of two which represent the numbers of binary values that can be created with the current digit, combined with all lesser significant digits to the right.

2^8.....2^7.....2^6.....2^5.....2^4.....2^3.....2^2.....2^1
128.....64.......32.....16...........8.........4.........2.......1 *These are the bit weights for each binary digit – not the actual powers of 2 in the line above*
1...........0..........1......1............0..........1........1.......1

So to take an example, if we consider the third digit from the right, which has a bit weight of 4, if we take the 4 position as well as the remaining lesser significant bits (2s position and 1s position), we have a total of three binary digits to work with. From these three digits, (4s, 2s, 1s) we can represent 2^3=8 different binary values from (0 thru 7 in decimal)

Here is how it works out for all eight positions

Position # from right....Bit Weight...Number of values we can represent (inclusive of all lesser significant digits)
---------------------------------.....-------------......------------------------------------------------------------------------------------------------------------------------
1...........................................1..........................2^1 = 2 ................ (Decimal 0 or 1)
2...........................................2..........................2^2 = 4 ................ (Decimal 0 – 3)
3...........................................4..........................2^3 = 8 ................ (Decimal 0 – 7)
4...........................................8..........................2^4 = 16 ..............(Decimal 0 – 15)
5..........................................16.........................2^5 = 32 ..............(Decimal 0 – 31)
6..........................................32.........................2^6 = 64 ..............(Decimal 0 – 63)
7..........................................64.........................2^7 = 128 ............(Decimal 0 – 127)
8.........................................128........................2^8 = 256 ............(Decimal 0 – 255)

Thanks again for viewing our videos, I hope this clears things up a bit.

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