Department of Electronics and Telecommunication Engineering

A Seminar on

“Floating point arithmetic unit

Implemented on FPGA using VHDL”

Guided byProf. H. M. Raza

Brief outline:

IEEE 754 format

Floating point unit

VHDL

FPGA

EDA Tools and softwares

Design of arithmetic units

Conclusion

Introduction to Floating Point IEEE 754Standard

Established in 1985 by IEEE

It has mainly two format

• Single Precision (32-bit)

• Double Precision(64-bit)

IEEE 754 single precision format

𝑁 = (−1)𝑆1.M*2𝐸−127

Mantissa (M)Mantissa (M)

Conversion Examples

Consider 9.5 is to be converted in standard IEEE754 format.

9.5 can be represented in binary as 1001.10

After normalization 1.00110*23

Biasing is to be done to exponent 1.00110*23+127

Similarly -12.076 can be represented as:

9.5 = 0 10000010 00110000000000000000000

-12.076 = 1 10000010 10000010011011101110101

Conversion of IEEE754 to decimal

1 1011 0110 01100000000000000000000

−𝟏 𝟏 × 𝟐𝟏𝟎𝟏𝟏𝟎𝟏𝟏𝟎−𝟎𝟏𝟏𝟏𝟏𝟏𝟏𝟏 × 𝟏. 𝟎𝟏𝟏= −𝟏. 𝟑𝟕𝟓 × 𝟐𝟓𝟓

= −49539595901075456.0

= −4.9539595901075456 ×𝟏𝟎𝟏𝟔

What is ALU?

It is Arithmetic and logical unit

In simple words any unit which performs the

required mathematical computations

Limitations of basic ALU

It operates only on Integer values, hence less

precision.

When forced to be operated on floating

point numbers then it results in slow

operations and lags in accuracy

Floating point arithmetic unit

FPAU is a arithmetic unit which is capable to

compute the floating point numbers (real

numbers)

Floating-point operations are often pipelined,

which increases the speed of operation.

What is FPGA?

• It is a semiconductor device that can be

programmed after manufacturing.

• The FPGA-architecture consists of many logic

modules, which are placed in an array-

structure

FPGA architecture

Significant characteristics for the FPGA-architecture

Array of logic-modules

Different logic-modules possible

Routing-channels physically exits between

logic-modules

Every logic-module can be interconnected to

any other logic-modul or I/O-module

Overview of VHDL

VHDL stands for Very High Speed Integrated

Circuit Hardware Description Language

VHDL is widely used to model digital systems

VHDL was originated in early 1980’s and was

standardized in 1987 by the IEEE

VHDL features

Structural Specification

Support for Design Hierarchy

Library Support

Support for Concurrent and Sequential Statements

Type Declaration

Use of subprograms

Design flow

The design file is written in VHDL language with the

extension .vhd and often named as its ENTITY’s name.

The major steps in design flow are:

Compilation

Optimization

Place-and-route

VHDL Constructs

Entity definition

Architecture definition

Configuration

Process

Subprogram

Package

A VHDL design can be broken into multiple files. Each file contains

entity and architecture definitions, or packages.

VHDL Code Structure

Entity Declaration

Defines input/output ports

Architecture Declaration

Defines what the component does Variables, Signals, Constants defines

Component Mapping

Interconnects previously defined components/entities.

Different modeling schemes in VHDL

Behavioral

defines outputs as function of input Algorithms

but no implementation

Structural

Implements behavior by connecting components

with known behavior

Example

entity andgate is

Port ( a : in STD_LOGIC;

b : in STD_LOGIC;

c : out STD_LOGIC);

end andgate;

architecture Behavioral of andgate is

Begin

c <= a AND b;

end Behavioral;

EDA tools and softwares used

Xilinx ISE design suit 14.7

This software is used to synthesize and simulate the VHDL code

developed.

Target device: Atlys Spartan-6 Academic Development Kit

Spartan-6 XC6SLX45 FPGA

6,822 Spartan-6 logic slices , 43,661 Spartan-6 logic cells

Integrated Memory Controller Block (MCB)

2,088 Kbits of block RAM

Design and implementation of FPAU

In top-down design approach FPAU is designed

for four arithmetic modules, addition,

subtraction, multiplication and division.

Selection of any of the above functions in done

with the operation code (Op)

Block diagram of FPAU

Input output information

A,B : input operands

Op : input operation code

Clk : input clock

R : Output Result

Function of Operation Code(Op)

Op(1) Op(0) Operation

0 0 Addition

0 1 Subtraction

1 0 Multiplication

1 1 Division

Algorithm for addition/subtraction

Step 1: Take difference of two exponents. Take the larger exponent as the tentative exponent of the result.

Step 2: Shift the Mantissa of the number with the smaller exponent, right through a number of bit positions that is equal to the difference of exponents.

Step 3: Add/subtract the two Mantissas as per sign bits and instruction and take the result of two as the tentative mantissa of result.

Step 4: Normalization of exponent and mantissa

Algorithm for Multiplication

Step 1: Add two exponents. Take the result tentative exponent of the result.

Step 2: Multiply two mantissas

Step 3: Normalization

Step 4: set the sign bit

Block diagram of multiplier/divider

RESULTS

Inferred 1 Multiplier(s).

Inferred 31 Adder/Subtractor(s).

Inferred 256 D-type flip-flop(s).

Inferred 2 Comparator(s).

Inferred 141 Multiplexer(s).

Timing Summary

Minimum period: 7.936ns (Maximum Frequency: 126.004MHz)

Synthesis summary

Simulation results while performing addition

Simulation results while performing multiplication

Conclusion

Synthesis of the Floating Point Unit targeted for

the FPGA device had been done using Xilinx-ISE

design suit 14.7. Synthesis result revels approximate

05% resource utilization i.e. 404 slices (202 CLB’s).

Correspondingly the logic verification of FPU is done

using ModelSim DE edition.