To use bitwise logic in the application of decoding IEEE754-encoded 32-bit values, displaying the decoded result.

Please consult the following resources to get a better feel on floating point and the IEEE754 standard:

• https://en.wikipedia.org/wiki/IEEE_754
• https://www.puntoflotante.net/FLOATING-POINT-FORMAT-IEEE-754.htm
• sciencedirect
• https://www.h-schmidt.net/FloatConverter/IEEE754.html

Much of our experience transacting in numbers on the computer has been with whole number/integer data. The format for unsigned data is straightforward.

Signed quantities undergo a process known as two's complement, which can be encoded/decoded to decipher the value stored within.

Floating point data also has an encoding scheme for storage. There are actually a few different floating point standards. One of the common, classic ones frequently found in use is that of IEEE754, which we will focus on in this project.

Walking through the decoding scheme, we'll start with an instance of IEEE754-encoded data: 0xC378C000

The first step is to visualize it in binary so we can proceed to divide it into its distinct components. Doing a simple hexadecimal to binary conversion yields:

Then, we carve up that 32-bit value according to the IEEE754 standard:

In this example, we have 1000 0110 or 0x86 in our exponent section.

What we do now is take that value, and subtract a 0x7F from it to get our actual exponent value:

• 0x86-0x7F = +7

We then start to setup our whole number value, which conceptually is to the immediate left of the mantissa. We assign a 1 to it by default. As a result, our floating point value (in binary) is currently:

• 1 . 111 1000 1100 0000 0000 0000

If our exponent value is positive, we LEFT SHIFT by that many bits. If negative, we RIGHT SHIFT.

In our case, our exponent value was a +7, so we will LEFT SHIFT by 7. Each bit that goes off the left end of the mantissa pops over into the value to the left of the decimal point.

Step-by step, our 24 total bits will progress as follows:

• original: 1 . 111 1000 1100 0000 0000 0000
• left shift by 1 (1): 11 . 11 1000 1100 0000 0000 0000
• left shift by 1 (2): 111 . 1 1000 1100 0000 0000 0000
• left shift by 1 (3): 1111 . 1000 1100 0000 0000 0000
• left shift by 1 (4): 11111 . 000 1100 0000 0000 0000
• left shift by 1 (5): 111110 . 00 1100 0000 0000 0000
• left shift by 1 (6): 1111100 . 0 1100 0000 0000 0000
• left shift by 1 (7): 11111000 . 1100 0000 0000 0000

The value we have to the left of the decimal point is 11111000, which when converted to decimal is 248.

We prefix the sign to this (1 indicates negative, which in this example it was), so: -248.

Now, to get the component to the right of the decimal point, we basically add together the bit positions, which correspond to 1/2^-position, where position starts at 1.

So, with our current value of 1100 0000 0000 0000, we have exactly 2 values containing a 1. Positions 1 and 2.

According to our formula:

• fraction = 0
• fraction = fraction + (1/(2^-1))
• fraction = fraction + (1/(2^-2))

As it turns out, (1/(2^-1)) = 0.5, and (1/(2^-2)) = 0.25, so:

• fraction = 0
• fraction = 0 + 0.5 = 0.5
• fraction = 0.5 + 0.25 = 0.75

We them put everything together:

• - 248 . 75

Therefore, 0xC378C000 decodes as -248.75

Your task is to write a program that will take in various encoded IEEE754 binary values, and to decode and ultimately display the decoded value.

You will be given a distinct list of floating point values that you will have to decode.

You will want to go here to edit and fill in the various sections of the document:

• https://lab46.g7n.org/notes/discrete/fall2024/projects/blf0

To be successful in this project, the following criteria (or their equivalent) must be met:

• Project must be submit on time, by the deadline.
  • Late submissions will lose 33% credit per day, with the submission window closing on the 3rd day following the deadline.
• Executed programs must display in a manner similar to provided output
  • output formatted, where applicable, must match that of project requirements
• Processing must be correct based on input given and output requested
• Output, if applicable, must be correct based on values input
• Code must be nicely and consistently indented
• Code must be consistently written, to strive for readability from having a consistent style throughout
• Code must be commented
  • Any “to be implemented” comments MUST be removed
    • these “to be implemented” comments, if still present at evaluation time, will result in points being deducted.
    • Sufficient comments explaining the point of provided logic MUST be present
• No global variables (without instructor approval), no goto statements, no calling of main()!
• Track/version the source code in your lab46 semester repository
• Submit a copy of your source code to me using the submit tool by the deadline.

Let's say you have completed work on the project, and are ready to submit, you would do the following:

lab46:~/src/SEMESTER/DESIG/PROJECT$ submit DESIG PROJECT file1 file2 file3 ... fileN

You should get some sort of confirmation indicating successful submission if all went according to plan. If not, check for typos and or locational mismatches.

I'll be evaluating the project based on the following criteria:

52:blf0:final tally of results (52/52)
*:blf0:implementation builds cleanly [13/13]
*:blf0:output conforms to specifications [13/13]
*:blf0:processing is correct, and to specifications [13/13]
*:blf0:provided example worked through on documentation [13/13]

• each class member is to participate in the contribution of relevant information and formatting of the documentation
  • minimal member contributions consist of:
    • near the class average edits (a value of at least four productive edits)
    • near the average class content change average (a value of at least 1024 bytes (absolute value of data content change))
    • no zero-sum commits (adding in one commit then later removing in its entirety for the sake of satisfying edit requirements)
  • adding and formatting data in an organized fashion, aiming to create an informative and readable document that anyone in the class can reference
  • content contributions will be factored into a documentation coefficient, a value multiplied against your actual project submission to influence the end result:
    • no contributions, co-efficient is 0.50
    • less than minimum contributions is 0.75
    • met minimum contribution threshold is 1.00

• Solutions not abiding by spirit of project will be subject to a 50% overall deduction
• Solutions not utilizing descriptive why and how comments will be subject to a 25% overall deduction
• Solutions not utilizing indentation to promote scope and clarity or otherwise maintaining consistency in code style and presentation will be subject to a 25% overall deduction
• Solutions not organized and easy to read (assume a terminal at least 90 characters wide, 40 characters tall) are subject to a 25% overall deduction