Design of Carry Select Adder using BEC and Common Boolean Logic

Carry Select Adder (CSLA) is known to be the fastest adder among the conventional adder structure, which uses multiple narrow adders. CSLA has a great scope of reducing area, power consumption, speed and delay. From the structure of regular CSLA using RCA, it consumes large area and power. This proposed work uses a simple and dynamic Gate Level Implementation which reduces the area, delay, power and speed of the regular CSLA. Based on a modified CSLA using BEC the implementation of 8-b, 16-b, 32-b square root CSLA (SQRT CSLA) architecture have been developed. In order to reduce the area and power consumption in a great way we proposed a design using binary to excess 1 converter (BEC). This paper proposes an dynamic method which replaces a BEC using Common Boolean Logic.

Sonic Eddy Model of the Turbulent Boundary Layer

The effects of Mach number on the skin friction and velocity fluctuations of the turbulent boundary layer are considered through a sonic eddy model. Originally proposed for free shear flows, the model assumes that the eddies responsible for momentum transfer have a rotation Mach number of unity, with the entrainment rate limited by acoustic signaling. Under this assumption, the model predicts that the skin friction coefficient should go as the inverse Mach number in a regime where the Mach number is larger than unity but smaller than the square root of the Reynolds number. The velocity fluctuations normalized by the friction velocity should be the inverse square root of the Mach number in the same regime. Turbulent transport is controlled by acoustic signaling. The density field adjusts itself such that the Reynolds stresses correspond to the momentum transport. In contrast, the conventional van Driest–Morkovin view is that the Mach number effects are due to density variations directly. A new experiment or simulation is proposed to test this model using different gases in an incompressible boundary layer, following the example of Brown and Roshko in the free shear layer.

Rationalizing Denominators Using Gröbner Bases

The problem of rationalizing denominators for two types of fractions is discussed in the paper. By using the theory and algorithms of Gröbner bases, we first introduce a method to rationalize the denominators of fractions with square root and cube root, and then, for the denominators with higher radical of the general form, the problem of rationalizing denominators is converted into the related problem of finding the minimal polynomials. Some interesting results and an executable algorithm for rationalizing the denominator of these type fractions are presented. Furthermore, an example is also established to illustrate the effectiveness of the algorithm.

A note on machine method for root extraction

The present investigation deals with the critical study of the works of Lancaster and Traub, who have developed $n$th root extraction methods of a real number. It is found that their developed methods are equivalent and the particular cases of Halley's and Householder's methods. Again the methods presented by them are easily obtained from simple modifications of Newton's method, which is the extension of Heron's square root iteration formula. Further, the rate of convergency of their reported methods are studied.