Scribe-Pad

strict_inequalities

Ramasamy Chandramouli — 2008-05-04T08:51:40-05:00

Let us consider a sequence of integers, Sequence - A We form another sequence that is roughly half the length of the above sequence, Sequence - B We cannot of course ensure the same inequality to hold for the above , but in case if we want the above inequality to hold, we need to change values of some of the . Assuming that we change , in order to meet the constraint in , and we proceed further to create another sequence , in the following way as is obtained from . This process is not inf…

sequence_encounter - created

Ramasamy Chandramouli — 2008-05-03T16:59:51-05:00

Sequences are so fascinating in their beauty. The changes in patterns and the dynamics would tie us up for the whole lifetime. It is hard to be an exception to avoid sequences. Here are few encounters with them. Journey through the sequences are so fascinating that you would cross the meadows that look the same but different.

welcome

Ramasamy Chandramouli — 2008-04-28T13:36:25-05:00

Aroused by curiosity, and by the way of pleasure in finding things out, certain scribblings of this amateur has been recorded. Thoughts always flow. There are designed to be that way. Its upto the system to hold the thoughts for itself that it fades away with time or to trust upon an illusive storage unit miles away which depends on the storage action using magnetics in a box. The system in me decides to choose the later, thus would be an open book and would record the thoughts that seems worthy…

solve_it_archives

Ramasamy Chandramouli — 2007-06-21T04:40:33-05:00

This section is a collection of problems that range from simple bit-related problems to digital designs. As such, no restriction is placed on proposing the problems. We do like to stick with few basic principles in this arena. Here are they: * Anyone can propose a problem and anyone can solve. * Take care not to repeat the problems that were already solved or proposed. * Make sure to maintain the count in this page to reflect the number of problems. * Its not demanding on the problem …

joy_of_lisping

Ramasamy Chandramouli — 2007-04-17T09:21:02-05:00

Not for fun, but actually started to have some fun with cutty parenthesis lurking around the code, has a more ‘machine’ like flavour coding with those symbols. But the serious fun has become a bit serious after grabbing the beauty of the Lisp. The beauty of Lisp is its limited types/keywords, with flexible extension for building maximal blocks. Here are some snippets written for fun but could be put under analysis. There exists lot of variants of Lisp for the snippets presented below is writ…

poly_infinite_products - created

Ramasamy Chandramouli — 2007-04-09T09:46:11-05:00

Polynomials are undoubtedly a beautiful representation of abstraction by humans. Here we restrict our explorations in polynomials that carry integral powers/coefficients. Here are few simpler polynomials and their factorizations. Some examples For now, leaving all the rules of convergence, that play a tricky role of deciding the expansions, we take it for granted that some kind of convergence rule would hold and go on to investigate on the patterns of expansions in these polynomials.

week-6 - created

Ramasamy Chandramouli — 2007-04-09T02:38:28-05:00

String Compression Dexter is out with a crazy idea of designing a string compression algorithm. He wanted to store distinct symbols and any combination/permutation of that symbols is valid and hence need to keep track of all of them. So, he decides to proceed in this way:

week-5 - created

Ramasamy Chandramouli — 2007-04-09T02:37:50-05:00

1. Shuttles in Space Consider the scenario where the people of this world goes into a ET-spree for search of life out of earth. They send N space shuttles out in different directions in search of life. To maintain the team of shuttles, they need to communicate with each other so that they exchange the information of their present location in space and their guess on existance of life on the location they presently stand.

week-4 - created

Ramasamy Chandramouli — 2007-04-09T02:37:20-05:00

1. Complex, is it so complex? Consider the scenario of complex multiplication. The basics of complex algebra tells (a + ib)(c + id) = (ac - bd) + i(ad + bc). Here we see, we do 4 multiplications and 2 additions. Consider architectures where multiplication operations are much costlier than addition. Can we do the above multiplication in a compact form so that the multiplication gets reduced? At which scenario its better to go for that method with less multiplication?

week-3 - created

Ramasamy Chandramouli — 2007-04-09T02:36:45-05:00

1. Palindromic Binary Strings Let us consider the k-bit binary strings. We inspect the palindromic strings of length k. Here are few analysis: k-bits Palindromic Strings Total 1 0×0, 0×1 2 2 0×00, 0×11 2 3 0×000, 0×010, 0×101, 0×111 4 And the above goes like this. What we are interested in is that, how many binary palindromic strings exists for a given length, N? Can we have an expression for the above in terms of N?

week-2 - created

Ramasamy Chandramouli — 2007-04-09T02:35:57-05:00

1. Is a Zero? Given a number (8/16/32/64 bit, +/-ve or 0) find if its a zero-valued number. Pretty easy task isnt? But wait! Here are a few restrictions on that: * No logical operators should be used [!, >, >=, <, <=, &&, ||, ==] * No if’s/for’s/while’s etc. * Only operators allowed: [ &, |, ~, ^, +, -, >>, << ]

week-1 - created

Ramasamy Chandramouli — 2007-04-09T02:33:45-05:00

1. The Sequence Given the inputs I={1,3,5}, return outputs O={3,5,1}. Meaning, given I=1, return O=3, and so on. These are the constraints imposed: * No extra memory other than ‘I’ should be used to process. * Only operators available are: &, |, ~, ^, >>, <<, +, -. * No logical operators/if’s/for’s/while’s please.