Binary Math – Part I

As CCIE candidates, we are asked to do all sorts of things with access lists.  We have them in lots of different places, and use them in lots of different ways.  So many, sometimes, that it becomes very confusing to follow things!
Access-lists themselves aren’t really that bad.  Or are they?  When we use them with route-maps, occasionally we see permits in an access-list that are really used to deny the packet/route/whatever.  What’s up with that?
Remember that ACLs are simply a matching mechanism.  Something either DOES (permit) or DOES NOT (deny) match the list.  Now, what we do with that matching status depends on how we use the ACL.  As an interface-based packet filter, it truly is a permit or deny of the packet!  In a route-map, it would depend on whether the route-map clause is a permit one or a deny one, in which case anything MATCHING the ACL would follow that route-map permit or deny ability.
Now, within an access-list, we also have some difficult things to grasp.  I like to consider that lesson in binary math.  That may oversimplify it, because really all we are doing is counting a 0 or a 1.  How difficult can it be to count to one???  :)
All by itself, it’s not that difficult.  But the we’ll get some really obnoxious words thrown in like “in as few lines as possible” or “minimal configuration”.  That means we have to start thinking about how the router sees things.
Let’s start with some groupings or summaries, and get the ball rolling.
In as few lines as possible (which translates to “no overlap”) summarize:
There’s only four networks, so it should be a /22, right?  We learned that back in CCNA!  Well, not quite so fast, because there’s a bit-boundary in our way.   The best way to start with any of these tasks is to work with the binary and start to see the patterns.
31    00011111
32    00100000
33    00100001
34    00100010
Now, we may have seen some documents about performing an XOR function between the different entries.  This is kinda-sorta true.  From a pure logical construct, XOR measures between two different things.  Here we have four.  So would it be an XXXOR  or an XOROROR?  Either way, the point is we are beyond the basic logical formula!
But it really isn’t as bad as it may sound!  Think about it in very simplistic terms!  Next, we look at what things are the same and which are different.  Well, between 31 and 32 we see LOTS of things that are different.  6 bits, in particular, have different values.  When we create an ACL binary mask, the 0-bit means “stay the same” while a 1-bit means “different” or “don’t care”.
So just on two values with 6 bits of difference, we could come up with a mask of 00111111 and it would work.  The problem we create, though, is the over-matching.  If you take 2 to the power of the total number of 1-bits in your mask, you’ll find the total number of matches for the mask.
In this case, 2^6 yields 64 matches to that mask.  We only have four things to group, so that’s not cool.  So we won’t be able to get our summary in one line!!  Leave 31 by itself then.  Look at 32, 33 and 34.
There are two bits (the 1-position and 2-position) that are different.  Here with a mask of 00000011 and two bits set to the 1-bit value, there will be a total of four matches to the mask (2^2).  Still more than we want, as there’s only three lines left after setting aside “31″!
But, here’s where we start to look at multiple ways to accomplish the task!
access-list 10 permit
access-list 10 permit
access-list 10 permit

access-list 10 permit
access-list 10 deny
access-list 10 permit

Both results give us a total of three lines as the tightest configuration we can get.  The difference is that one of them over-permits, but we deny those non-listed things first!  So if your lab task says there “must be at least one ‘deny’ statement” then this is it.
The bottom line is no more, no less though!   So let’s add to that list.
In as few lines as possible (which translates to “no overlap”) summarize:
We know we’ll run into the same basic quandary with “31″ and the others as we did before.  But what about the rest?  Back to binary.
31    00011111
32    00100000
33    00100001
34    00100010
35    00100011
36    00100100
37    00100101
Counting 31 off on its own, we notice there are three bits that have varying values from 32 through 37.  The 1-bit, 2-bit and 4-bit positions.  So if we used a mask of 00000111, that would cover all of those three bits.
2^3 to check the mask though tells us there would be eight matches.  There’s only six values listed to match.  We want no more, no less!  Notice that 32 through 35 has two bits varying between them.  A mask of 00000011 would match ONLY those four.  And a mask of 00000001 would match ONLY the 36 and 37.
So we can use:
access-list 11 permit
access-list 11 permit
access-list 11 permit

What if we were told that we must have at least one DENY statement in the ACL?
Oh, those obnoxious requirements!  Think like we did with the first one with the over-permitting.  Let’s go back to the 00000111 mask.  What extra values come into play there?
With a mask, we are saying we permit any and all of the variants with the bits.  No matter where they fall in the mask, we should substitute values in to see them!
With three bits, we need:
The “110″ and “111″ matches are not in our list.  That would be 38 and 39.
38    00100110
39    00100111
Those can be summarized as well, so here’s a list with a deny:
access-list 11 permit
access-list 11 deny
access-list 11 permit

Exactly the same list is being permitted as before.  With no more or no less.
Now, let’s start talking about non-contiguous matching!  Because that’s where life becomes more interesting.  We’re following the same rules though.
What if we are instructed to pick only the even /24 networks from
As I said, the rules don’t change here, it’s just “different” than we may be used to building masks for.  We just aren’t drawing a “line” to separate network from host.  That’s the CCNA version of access-lists.  While it’s technically true, it’s not the entire truth!  As a CCIE we are expected to know more!
So we can go back and start breaking all the even  numbers up into binary to start to see our patterns.
0    00000000
2    00000010
4    00000100
6    00000110
8    00001000
10    00001010
12    00001100
14    00001110
16    00010000
Blah, blah, blah…  You get the idea.  Keep going if you want, but you should already get the pattern.  The ONLY bit that WILL NEVER change is the 1-bit position, which will always be a zero.
Our mask will consist of seven “don’t care” bits and one “must be the same” bit. 11111110 will work perfectly fine.   Now, here’s the catchy part.  What do you put as the ‘network’ portion of the ACL?
Well, let’s expand on that “network” name….  Again, very CCNA explanation.  What really is happening is that your ACL has a “binary starting point” and a “binary mask” to go with it.
So we need to SET our values, then provide the rules for what can change or what cannot.
access-list 12 permit will permit all of the EVEN /24′s there.
Why did we put “.0″ as the fourth octet?  Because the question asked for /24′s, which implies this will be used in a routing protocol.  All /24 network advertisements must have “.0″ as the fourth octet and it cannot change.  If it were a security question asking for hosts in the even numbered networks, then we would use a mask.
What if we wanted the ODD networks out of the same range?
You can work out the binary if you want, but you will find that the mask will actually be the same thing.  The only difference here is that our STARTING POINT changes.
access-list 13 permit will permit all of the ODD /24′s!!!
So our big lessons here are:
- All bits are treated individually (no “line” to draw)
- The logical least number of lines may include over-permission with a deny first
- It’s not a “network”, but rather a binary starting point.
- Don’t forget to check the mask using 2^(# of 1-bits in the mask) forumla!

Some extra ones to think about, and we’ll see who gets the answers first.
1.  Allow packets from all hosts in every fourth /24 network from
2.  In as few lines as possible, permit only the following networks (assume it will be a distribute-list):
3. In as few lines as possible, allow access from all hosts in the network except .93 through .106.  You are not allowed to use any “deny” statements.
Be sure to comment with your answers, no comments will show up until the contest ends.  The first person with all three answers correct will win 60 tokens!!! Whether you are renting racks of equipment for any track or working on graded Mock Labs, those tokens sure come in handy!


About US

Network Bulls is Best Institute for Cisco CCNA, CCNA Security, CCNA Voice, CCNP, CCNP Security, CCNP Voice, CCIP, CCIE RS, CCIE Security Version 4 and CCIE Voice Certification courses in India. Network Bulls is a complete Cisco Certification Training and Course Coaching Institute in Gurgaon/Delhi NCR region in India. Network Bulls has Biggest Cisco Training labs in India. Network Bulls offers all Cisco courses on Real Cisco Devices. Network Bulls has Biggest Team of CCIE Trainers in North India, with more than 90% of passing rate in First Attempt for CCIE Security Version 4 candidates.
  • Biggest Cisco Training Labs in India
  • More than 90% Passing Rate in First Attempt
  • CCIE Certified Trainers for All courses
  • 24x7 Lab Facility
  • 100% Job Guaranteed Courses
  • Awarded as Best Network Security Institute in 2011 by Times
  • Only Institute in India, to provide CCIE Security Version 4.0 Training
  • CCIE Security Version 4 Training available
  • Latest equipments available for CCIE Security Version 4

Network Bulls Institute Gurgaon

Network Bulls Institute in Gurgaon is one of the best Cisco Certifications Training Centers in India. Network Bulls has Biggest Networking Training and Networking courses labs in North India. Network Bulls is offering Cisco Training courses on real Cisco Routers and Switches. Labs of Network Bulls Institute are 24x7 Available. There are many coaching Centers in Delhi, Gurgaon, Chandigarh, Jaipur, Surat, Mumbai, Bangalore, Hyderabad and Chennai, who are offering Cisco courses, but very few institutes out of that big list are offering Cisco Networking Training on real Cisco devices, with Live Projects. Network Bulls is not just an institute. Network Bulls is a Networking and Network Security Training and consultancy company, which is offering Cisco certifications Training as well support too. NB is awarded in January 2012, by Times, as Best Network Security and Cisco Training Institute for the year 2011. Network Bulls is also offering Summer Training in Gurgaon and Delhi. Network Bulls has collaboration with IT companies, from which Network Bulls is offering Networking courses in Summer Training and Industrial Training of Btech BE BCA MCA students on real Live projects. Job Oriented Training and Industrial Training on Live projects is also offered by network bulls in Gurgaon and Delhi NCR region. Network Bulls is also providing Cisco Networking Trainings to Corporates of Delhi, Gurgaon, bangalore, Jaipur, Nigeria, Chandigarh, Mohali, Haryana, Punjab, Bhiwani, Ambala, Chennai, Hyderabad.
Cisco Certification Exams are also conducted by Network Bulls in its Gurgaon Branch.
Network Bulls don't provide any Cisco CCNA, CCNP simulations for practice. They Provide High End Trainings on Real topologies for high tech troubleshooting on real Networks. There is a list of Top and best Training Institutes in India, which are providing CCNA and CCNP courses, but NB has a different image from market. Many students has given me their feedbacks and reviews about Network bulls Institute, but there were no complaints about any fraud from this institute. Network Bulls is such a wonderful place to get trained from Industry expert Trainers, under guidance of CCIE Certified Engineers.

About Blog

This Blog Contains Links shared by sites: Cisco Guides, Dumps collection, Exam collection, Career Cert, Ketam Mehta,


Cisco Networking Certifications Training

Cisco Training in Delhi

ccna training in gurgaon. ccnp course institute in gurgaon, ccie coaching and bootcamp training near gurgaon and delhi. best institute of ccna course in delhi gurgaon india. network bulls provides ccna,ccnp,ccsp,ccie course training in gurgaon, new delhi and india. ccsp training new delhi, ccie security bootcamp in delhi.

Testimonials : Network Bulls

My Name is Rohit Sharma and i Have done CCNA and CCNP Training in Gurgaon Center of Network Bulls and it was a great experience for me to study in Network Bulls.

Cisco Networking Certifications

Myself Komal Verma and i took CCSP Training from Network Bulls in Gurgaon. The day i joined Network Bulls, the day i get addicted with Networking Technologies and I thank Mr. Vikas Sheokand for this wonderful session of Networking. :)
I must say that Network Bulls is Best Institute of CCNA CCNP CCSP CCIE Course Training in Gurgaon, New Delhi and in India too.
Komal Verma

About a wonderfull CCIE Training Institute in Gurgaon

I am Kiran shah from New Delhi. I have recently completed my CCNA CCNP & CCIE Training in Gurgaon from Network Bulls and i recommend Network Bulls for Cisco Training in India.

Kiran Shah

Cisco Coaching and Learning Center

Disclaimer: This site does not store any files on its server. I only index and link to content provided by other sites. If you see any file on server that is against copy right you can inform me at (sidd12341 [at] I will delete that materials within two days. This Website is not official Website of any Institute like INE, Network Bulls, IP Expert. Thanks

CCIE Security Version 4

Cisco Finally updated CCIE Security Lab exam blueprint. WSA Ironport and ISE devices are added in CCIE Security Version 4 Lab Exam Syllabus Blueprint. In Updated CCIE Security Version 4 Syllabus blueprint, new technologies like Mobile Security, VoIP Security and IPV6 Security along with Network Security, are added. As in CCIE Security Version 3 blueprint, Cisco had focused on Network Security only, but now as per market demand, Cisco is looking forward to produce Internet gear Security Engineer, not only Network Security engineers.
In CCIE Security Version 4 Bluerpint, Lab Exam is going to be more interested than before. What is Difference in CCIE Security Version 3 and Version 4? Just go through the CCIE Security Version 4 Lab Equipment and Lab Exam Syllabus Blueprints and find out!