Table of Contents

Corning Community College

CSCS2330 Discrete Structures

PROJECT: Bitwise Logic Floats (BLF0)

OBJECTIVE

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

READING

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

BACKGROUND

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.

binary layout of IEEE754 (sourced from wikipedia article)

Process

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:

C 3 7 8 C 0 0 0
1100 0011 0111 1000 1100 0000 0000 0000

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

sign (bit 31) exponent (bits 30-23) mantissa (bits 22-0)
1 100 0011 0 111 1000 1100 0000 0000 0000

Determine the exponent

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:

Set up our mantissa for exponent processing

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:

bit shift by exponent

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:

determine value to the left of the decimal point

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.

determine the fractional value

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:

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

We them put everything together:

Therefore, 0xC378C000 decodes as -248.75

TASK

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.

EDIT

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

BLF0

LOGIC

key value
0 false
1 true

Truth tables consist of one or two inputs (A, B), and an output (X)

AND
A B X
0 0 0
0 1 0
1 0 0
1 1 1
OR
NOT
XOR
NAND
NOR
XNOR
BITWISE LEFT SHIFT
BITWISE RIGHT SHIFT
BIT MASKING

BITWISE LOGIC

BITWISE AND
BITWISE OR
BITWISE NOT
BITWISE XOR
 

SUBMISSION

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

Submit Tool Usage

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.

RUBRIC

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]

Pertaining to the collaborative authoring of project documentation

Additionally