Abstract: The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.
Abstract: Timing driven physical design, synthesis, and
optimization tools need efficient closed-form delay models for
estimating the delay associated with each net in an integrated circuit
(IC) design. The total number of nets in a modern IC design has
increased dramatically and exceeded millions. Therefore efficient
modeling of interconnection is needed for high speed IC-s. This
paper presents closed–form expressions for RC and RLC
interconnection trees in current mode signaling, which can be
implemented in VLSI design tool. These analytical model
expressions can be used for accurate calculation of delay after the
design clock tree has been laid out and the design is fully routed.
Evaluation of these analytical models is several orders of magnitude
faster than simulation using SPICE.