# Digital Arithmetic

## Floating Point Architectures

In the previous tutorials, we have discussed about the fixed point architectures. Majority of FPGA based architectures are fixed point based. In the fixed point architectures, the number of bits reserved for integer and fractional part is fixed. Thus there is a limitation in representing wide range of numbers. This limitation results truncation error at …

## Fast Multiplication

The fast multiplication can be achieved in three general ways. The sequential multipliers sequentially generates the partial products and adds them with the previously stored partial products. In the second method, high speed parallel multipliers generate the partial products in parallel and adds them by a fast multi-operand adder. The third method corresponds to use …

## Square Root and Its Reciprocal

Square root is an important arithmetic operation which is useful in many signal processing algorithms. In implementation of signal processing algorithms, implementation of square root plays a crucial role. Similarly in many applications such as in implementation of QR decomposition using Gram-Schmidt algorithm, computation of square root reciprocal is preferred. In this tutorial we have …

## Division Algorithms

Division operation is the most complex operation to perform among all the arithmetic operations and it is also time consuming. The equation of a division operation is where N is the dividend, D is the divisor, Q is the Quotient and R is the remainder. The remainder R is less than D. In implementation of …

## CORDIC Algorithm

COordinate Rotation Digital Computer (CORDIC) is a simple and efficient algorithm to compute arithmetic, trigonometric and hyperbolic functions. In many fields such as DSP, image processing, communication or in industrial sectors, researchers are using CORDIC algorithm to optimize design performance. CORDIC was conceived in 1956 by Jack E. Volder thus it sometimes called as Volder’s …