A scientific representation of 30,064,771 is 3.0064771 x 10 7 , whereas 1.001 can be written as 1.001 x 10 0. Floating-Point Addition, IEEE-754, FPGA, Delay Optimization. INTRODUCTION: In digital systems IEEE-754 8 standard is used for representing the floating-point numbers and are of different types according to their mantissa bit length. There are half, single, double and quadruple precision binary numbers having a mantissa of bit length 16, 32.

In the previous tutorials, we have discussed about the fixed point architectures. VERILOG Source Code or/and Encrypted, or plain text EDIF netlist VHDL. The implementation is performed using XilinxвЂ™s Spartan 3 FPGAs. Index Terms: Field Programmable Gate Array, Hardware Implementation, Float Point Arithmetic, Xilinx, Verilog HDL. I.INTRODUCTIONQuantizing floating-point algorithms to fixed-point for efficient FPGA or ASIC implementation requires many steps and numerical considerations. Converging on the right balance between arithmetic precision and hardware resource usage is an iterative process between algorithm and hardware design.

This limitation results truncation error at the output. Thus there is a limitation in representing wide range of numbers. In the fixed point architectures, the number of bits reserved for integer and fractional part is fixed.

On the other hand, floating point architectures provides better accuracy than fixed point architectures.The objective of this tutorial is to discuss the basics of floating point representation and the basic architectures for floating point arithmetic operation. Due to higher complexity, floating point architectures are not suitable for rapid prototyping. The reason behind this fact is that implementation of floating point architectures is complex. The usage of floating point representation in real time implementations is limited. The floating point representation solves this problem.Previously we have discussed about basics of floating point numbers in Digital System Design Basics. At some point further increase in word length can not be tolerable.

If normalized then the minimum number will beAll the floating point architectures designed here follows 16-bit data width. The minimum number is not normalized here thus it is actually minimum subnormal number. The range of the exponent is thus 0 to 15 (Neglecting the infinity which is not required).Example: Convert in floating point representation.Here the bit which is shown in bold is the hidden bit.Maximum number that can be represented isMinimum number that can be represented isBoth the numbers also can be negative.

We have avoided the rounding here as it adds more hardware and also it can be considered in fixed point. Floating Point to Fixed Point ConversionThus in this tutorial, all the major floating point architectures are discussed and implemented using Verilog structural coding.

Fpga Floating Point Verilog