FIXED-POINT TO FLOATING-POINT & FLOATING-POINT TO FIXED-POINT CONVERSION

Overview

This document describes the conversion process between fixed-point and floating-point representations. The system supports various data sizes and facilitates bidirectional conversion.

Applications

There are two primary applications:

1. Fixed to Floating-Point Conversion
2. Floating-Point to Fixed Conversion

Each application supports the following sizes:

• Floating-Point Sizes: 32-bit, 64-bit, 80-bit
• Fixed-Point Sizes (Integer & Fraction): 16-bit, 32-bit, 40-bit

Data Frame Structure

Packet Format

• 1st Byte: Application (2 bits), Size (3 bits), Packet (3 bits)
  • Application: 1 (Floating-Point to Fixed), 2 (Fixed to Floating-Point)
  • Size:
    • 1 (2 bytes integer & fraction, 4 bytes floating-point)
    • 2 (4 bytes integer & fraction, 8 bytes floating-point)
    • 3 (5 bytes integer & fraction, 10 bytes floating-point)
  • Packet: Packet 1, Packet 2
• 2nd - 5th Byte: Input Data (Integer, Fraction, Floating-Point)

---

Fixed-Point to Floating-Point Conversion

This conversion transforms a fixed-point integer and fraction into a floating-point representation.

Input/Output Formats

Size 1

Input packet :-

Ouput packet :-

• Application Selection, Size & Packet: First packet: 88
  • Application: 2 (2'b10)
  • Size: 1 (3'b001)
  • Packet: 0 (3'b000)
• Input: 2 bytes (integer & fraction)
  • Data: 2 bytes (integer), 2 bytes (fraction), 1 byte (reserved)
• Output: 4 bytes (floating point)
  • Data: 4 bytes (floating point), 1 byte (reserved)

Example

Input Details

• Decimal Value: 28.6528
• Integer Part: 28 → Hex: 00 1c
• Fractional Part: 0.6528 → Hex: a7 90

The input data is structured as follows:

Input  packet: 88 00 1c a7 90 00 

• 88 → Header/Identifier(application,size & packet)
• 00 1c → Integer representation (28)
• a7 90 → Fractional representation (0.6528)
• 00 → Reserved

The output data packet is structured as follows:

Output Packet: 88 41 E5 3C 80 00

• 88 → Header/Identifier(application,size & packet)
• 41 e5 3c 80 → Floating-point representation of 28.6528
• 00 → Reserved

Size 2

Input packet :-

Ouput packet :-

• Application Selection, Size & Packet:
  • First packet: 91, Second packet: 92
  • Application: 2 (2'b10)
  • Size: 2 (3'b010)
  • Packet: 1,2 (3'b001, 3'b010)
• Input: 4 bytes (integer & fraction)
  • Data Packet 1: 4 bytes (integer), 1 byte (reserved)
  • Data Packet 2: 4 bytes (fraction), 1 byte (reserved)
• Output: 8 bytes (floating point)
  • Data Packet 1: 5 bytes (floating point)
  • Data Packet 2: 3 bytes (floating point), 1 byte (reserved)

Example

Input  packet1: 91 00 00 00 1c 00
Input  packet2: 92 a7 90 00 00 00
Output packet1: 91 40 3c a7 90 00 
Output packet2: 92 00 00 00 00 00

Size 3

Input packet :-

Ouput packet :-

• Application Selection, Size & Packet:
  • First packet: 99, Second packet: 9a
  • Application: 2 (2'b10)
  • Size: 3 (3'b011)
  • Packet: 1,2 (3'b001, 3'b010)
• Input: 5 bytes (integer & fraction)
  • Data Packet 1: 5 bytes (integer)
  • Data Packet 2: 5 bytes (fraction)
• Output: 10 bytes (floating point)
  • Data Packet 1: 5 bytes (floating point)
  • Data Packet 2: 5 bytes (floating point)

Example

Input  packet1: 99 00 00 00 00 1C
Input  packet2: 9a a7 90 00 00 00
Output packet1: 99 40 03 ca 79 00
Output packet2: 9a 00 00 00 00 00

---

Floating-Point to Fixed-Point Conversion

This conversion transforms a floating-point number into its fixed-point integer and fraction components.

Input/Output Formats

Size 1

Input packet :-

Ouput packet :-

• Application Selection, Size & Packet: First packet: 48
  • Application: 1 (2'b01)
  • Size: 1 (3'b001)
  • Packet: 0 (3'b000)
• Input: 4 bytes (floating point)
  • Data: 4 bytes (floating point), 1 byte (reserved)
• Output: 2 bytes (integer & fraction)
  • Data: 2 bytes (integer), 2 bytes (fraction), 1 byte (reserved)

Example

Input Details

• Floation-point hex value: 41 e5 3c 80

The input data is structured as follows:

Input  packet: 48 41 e5 3c 80 00

• 48 → Header/Identifier(application,size & packet)
• 41 E5 3C 80 → Floating-point representation of 28.6528
• 00 → Reserved

The output data packet is structured as follows:

Output packet: 48 00 1c a7 90 00

• 48 → Header/Identifir(application,size & packet)
• Integer Part: 00 1c → Decimal: 28
• Fractional Part: a7 90 → Decimal: 0.6528
• 00 → Reserved

Size 2

Input packet :-

Ouput packet :-

• Application Selection, Size & Packet:
  • First packet: 51, Second packet: 52
  • Application: 1 (2'b01)
  • Size: 2 (3'b010)
  • Packet: 1,2 (3'b001, 3'b010)
• Input: 8 bytes (floating point)
  • Data Packet 1: 5 bytes (floating point)
  • Data Packet 2: 3 bytes (floating point), 2 bytes (reserved)
• Output: 4 bytes (integer & fraction)
  • Data Packet 1: 4 bytes (integer), 1 byte (reserved)
  • Data Packet 2: 4 bytes (fraction), 1 byte (reserved)

Example

Input  packet1: 51 40 3c a7 90 00
Input  packet2: 52 00 00 00 00 00
Output packet1: 51 00 00 00 1c 00
Output packet2: 52 a7 90 00 00 00 

Size 3

Input packet :-

Ouput packet :-

• Application Selection, Size & Packet:
  • First packet: 59, Second packet: 5a
  • Application: 1 (2'b01)
  • Size: 3 (3'b011)
  • Packet: 1,2 (3'b001, 3'b010)
• Input: 10 bytes (floating point)
  • Data Packet 1: 5 bytes (floating point)
  • Data Packet 2: 5 bytes (floating point)
• Output: 4 bytes (integer & fraction)
  • Data Packet 1: 5 bytes (integer)
  • Data Packet 2: 5 bytes (fraction)

Example

Input  packet1: 59 40 03 ca 79 00
Input  packet2: 5a 00 00 00 00 00
Output packet1: 59 00 00 00 00 1C
Output packet2: 5a a7 90 00 00 00