Whew, let's see if I can explain this - I kinda take this for granted
these days :-).

> How does one read addresses like 172.168.10/24 or 172.16.51.50/32 ?

  Many TCP/IP devices have adopted a shorthand method for indicating the
  subnet mask associated with a network address.
  
  The /24 indicates that 24 bits are reserved for the subnet mask.
  171.168.10.0/24 is shorthand for 171.168.10.0 255.255.255.0. 

  As you can see, this is  much easier method for representing IP network
  addresses and their associated masks.

  Basically, in this context, the /24 means that  what you are looking
  at is an entire Class C address space.

  The /32 means that you are looking at the address of a specific host 
  ( since there are only 32 bits available in an IP address and they are
    all being specified, there is none left for a subnet mask hence this
    must be a host address. )

  It is worthwhile to mention that IP addresses are composed of 4 octets (
  32 bits ) which is where the notation /24 ( 3*8 ) and 32 ( 4*8 ) comes
  from.
  Given that a class B address would be 128.10/16.

> In particular, what does the slash signify what does it do in the above
> case(s).

  the slash is a separator to indicate that the number following is the
  number of bits which are significant for the situation that is under
  consideration. 

  The number following the slash does not necessarily have to be a
  multiple of 8, and if it isn't then it is indicative of a subnetted IP
  address space.  

  "Prefix" is a shorthand way of referring to the number of bits in the
  address that are covered by the associated subnet mask. A non-subnetted
  Class C address has a 24-bit prefix by default. A subnetted Class C
  address with a mask of 255.255.255.240 has a /28 bit subnet mask
  and a 28-bit prefix. 

> If this is anywhere off topic for the list, personal e-mail will do too.

  Hope that helps somewhat.
  you might want to check out:

     http://www.cisco.com/cpress/cc/td/cpress/fund/primer/cb0708.htm

 which gives a pretty good answer to your question. Its also where I
 plagarized some of my explanation from :-)


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Larry Chin {[EMAIL PROTECTED]}      Technical Specialist - ISC
Sprint Canada                     2550 Victoria Park Avenue
Phone: 416.496.1644 ext. 4693     Suite 200, North York, Ontario
Fax:   416.498.3507               M2J 5E6
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