# The Subnet Training Guide

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1 The Subnet Training Guide A Step By Step Guide on Understanding and Solving Subnetting Problems by Brendan Choi v25 easysubnetcom

7 The Subnet Training Guide v25 easysubnetcom 101 add = six 110 add = seven 111 add = eight We can keep adding these binary numbers to infinity to write all numbers Here are some of the numbers, along with the exponential values (powers of 2) 0 = zero 1 = one = = two = = three 100 = four = = five 110 = six 111 = seven 1000 = eight = = nine 1111 = fifteen = sixteen = = seventeen = thirty-one = thirty-two = = thirty-three = five hundred and eleven = five hundred and twelve = = five hundred and thirteen = five hundred and fourteen Notice that in the Binary system, the exponentials (powers of 2) are reached a lot sooner, at 1, 4, 8, 16, 32 and so on In the Decimal system, we reach the exponentials (powers of 10) at 1, 10, 100, 1000 and so on 0 = zero Copyright 2009 Brendan Choi All Rights Reserved 7

8 The Subnet Training Guide v25 easysubnetcom 1 = one = = two 3 = three 9 = nine 10 = ten = = eleven 12 = twelve 99 = ninety-nine 100 = one hundred = = one hundred and one 998 = nine hundred ninety-eight 999 = nine hundred ninety-nine 1000 = one thousand = = one thousand and one When comparing the Decimal and Binary systems, we can see that the Decimal system uses more numerical symbols and the numbers increase their places from right to left a lot slower For Binary numbers, the numbers increase their places from right to left a lot faster For us, the Decimal system is a lot more easier to read and write To write the value "three thousand five hundred and seventy one" in decimal, we only need to write a few numbers, but we need to write a lot more numbers in binary Decimal = 3571 Binary = But computers calculate from electrical signals, that can be either "on" or "off" or positive or negative So it's more efficient for computers to use binary numbers to calculate In IP addressing and subnetting, we are dealing with octets, each with 8 possible bit places So we need to learn how to convert octets Let's convert an octet Example 11: Example of binary octet: (1 2 7 ) + (0 2 6 ) + (1 2 5 ) + (1 2 4 ) + (1 2 3 ) + (1 2 2 ) + (0 2 1 ) + (0 2 0 ) Like in our decimal number system, we compute from RIGHT to LEFT Notice that the first power of 2, the right most, is 2 0, and the last power of 2, the left most, is 2 7 Going from 0 to 7 is 8 bit places And 2 0 is just 1, which makes sense since the first place in a number system is the 1's place = 188 Copyright 2009 Brendan Choi All Rights Reserved 8

9 The Subnet Training Guide v25 easysubnetcom Therefore, = 188 Let's look at some Base-10 decimal numbers, and see how we really do the same thing Example 12: Example of decimal number: This number can be written as: ( ) + (4 10 3) + ( ) + ( ) + ( ) = Example 13: Example of decimal number: 1842 This number can be written as: (1 10 3) + ( ) + ( ) + ( ) = 1842 As you can see, the numbers written in our normal Base-10 decimal system are just powers of 10 In the Base-2 binary system, numbers are in powers of 2 Example 14: Example of binary octet: (0 2 7 ) + (1 2 6 ) + (1 2 5 ) + (1 2 4 ) + (0 2 3 ) + (1 2 2 ) + (0 2 1 ) + (1 2 0 ) = 117 Therefore, = 117 Example 15: Example of binary octet: (1 2 7 ) + (1 2 6 ) + (1 2 5 ) + (0 2 4 ) + (0 2 3 ) + (0 2 2 ) + (1 2 1 ) + (1 2 0 ) = 227 Therefore, = 227 Example 16: Example of binary octet: (0 2 7 ) + (0 2 6 ) + (1 2 5 ) + (1 2 4 ) + (1 2 3 ) + (1 2 2 ) + (0 2 1 ) + (0 2 0 ) = 60 Therefore, = 60 Notice that the lowest an octet can be is , which is just 0 And the highest is , which is just 255 Copyright 2009 Brendan Choi All Rights Reserved 9

14 The Subnet Training Guide v25 easysubnetcom The binary number for 235 is Example 115: Convert 109 to binary We start with 109, and find we can't divide by 128, so we skip it and continue to remainder remainder remainder remainder remainder 0 The binary number for 109 is Since the left most bit is 0, you might see this number written as also Remember we really count from RIGHT to LEFT Let's convert a number larger than 255 Example 116: Convert 457 to binary For this number, we have to go to 9 bit places, so the bit places go from 2 0 to remainder remainder remainder remainder remainder 0 So the binary number for 457 is Example 117: Convert 248 to binary remainder remainder remainder remainder remainder The binary number for 248 is Copyright 2009 Brendan Choi All Rights Reserved 14

23 The Subnet Training Guide v25 easysubnetcom Is there an easier way to find the first bit? Yes, the first bit is just minus the interesting octet = 256 subtract = 254 interesting octet = 2 increment In Example 122 above, the interesting octet of the subnet mask was 224, so the increment of the interesting octet in the network addresses was = = 256 subtract = 224 interesting octet = 32 increment As you can see, is just 2 8 = 256!! Notice that is a 9-bit number, not 8 bits As we saw earlier, the highest value an octet can have is 255 So you need an extra bit to get to 256 We see a similar behavior in our regular Base-10 decimal numbering system 10,000,000 subtract 9,999, ,000 = increment between all values xxxx000, like from 4,762,000 to 4,763,000 1,000,000 subtract 999, = increment of all values xxxx00, like from 823,700 to 823, ,000 subtract 99, = increment of all values xxx00, like from 60,500 to 60,600 10,000,000 subtract 9,900, ,000 = increment all values xx00000, like from 1,400,000 to 1,500,000 When doing subnetting problems on certification exams, the most important formula you have to remember is this: network address increment = (interesting octet of subnet mask) Another way to say this is that the increment is simply the first bit in the extra (subnet) bits! Copyright 2009 Brendan Choi All Rights Reserved 23

25 The Subnet Training Guide v25 easysubnetcom = = = = = = = = = = = = = = = When looking at the shaded area, think of it as a tumbler with numbers on it, like in a gas station meter or a car odometer The bits are tumbling and increasing from the RIGHT to the LEFT one by one Notice that the bits in the interesting octet wraps back to 0000 when it reaches 1111, and the octet to the LEFT increases by 1 Let's verify again that the increment in the interesting octet is the first bit in the extra bits = = (first bit greater than 0) = = = = (2 1 +1) = = ( ) = = ( ) = = ( ) 2 4 The increment is 2 4 = 16, and all the interesting octets of the network addresses are just multiples of the first bit! = 256 subtract = 240 interesting octet = 16 increment As we see again, the network increment = the interesting octet of the subnet mask Here are the first 4 broadcast addresses, where all the host bits are set to 1: = Copyright 2009 Brendan Choi All Rights Reserved 25

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