Hex and Binary

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Hex and Binary

Binary (Power of 2)

2 to the 0 = 1                                 2 to the 12^th = 4096
2 to the 1^st = 2                              2 to the 13^th = 8192
2 to the 2^nd = 4                             2 to the 14^th = 16384
2 to the 3^rd = 8                              2 to the 15^th = 32768
2 to the 4^th = 16                            2 to the 16^th = 65536
2 to the 5^th = 32                          2 to the 17^th = 131072
2 to the 6^th = 64                            2 to the 18^th = 262144
2 to the 7^th = 128                          2 to the 19^th = 524288
2 to the 8^th = 256                          2 to the 20^th = 1048576
2 to the 9^th = 512                          2 to the 21^st = 2097152
2 to the 10^th = 1024                     2 to the 22^nd = 4194304
2 to the 11^th = 2048

I only go up to 2 to the 22^nd because that is the maximum number of bits that can be borrowed when subnetting. Borrowing 22 bits from a Class A address will give us 4,194,302 networks. (4194304 -2)

128

64

32

16

8

4

2

1

The above represents one octet (8 bits). An IP address has 4 octets. The numbers are the binary value of each bit. If there is a 1 in any position, then the binary value of that bit is used. (00000001 would equal decimal 1. 00000011 would equal 3, and so on.)

If we had an address of 192.168.255.255, the binary values in each octet would be:

11000000.10101000.11111111.11111111

HEX (Power of 16) (Use the octet example above for all the binary calculations)

0 1 2 3 4 5 6 7 8 9 A(10) B(11) C(12) D(13) E(14) F(15)

Convert 17 DEC to HEX

convert to binary first
00010001 = 17

break down in groups of 4
0001 | 0001

convert each group of 4 to HEX
0001 = 1 | 0001 = 1

combine the results left to right (DO NOT add)
17 DEC = 11 HEX

Convert 58 DEC to HEX

00111010 = 58
0011 | 1010

0011 =3
1010 = A

58 DEC = 3A HEX

Convert 765 DEC to HEX

1011111101 = 765
To make even groups of 4, you must add leading zeros

001011111101 then break down into groups of 4

0010 | 1111 | 1101

0010 = 2
1111 = F
1101 = D
765 Dec = 2FD Hex

Convert HEX to DEC
3A to DEC

First convert to binary
3 = 00000011
A(10) = 00001010

starting with the first number (3), take only the significant digits - 11
then the significant digits from the second number - 1010
then combine them (from left to right) 111010 then convert to DEC 32+16+8+2 = 58

Convert BAD to Dec.

B = 11 = 00001011
A = 10 = 00001010
D = 13 = 00001101
101110101101 = 2989 Dec

Practice on your own using the above examples.