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haas:fall2023:discrete:projects:blf0 [2024/04/11 13:47] – [TASK] wedgehaas:fall2023:discrete:projects:blf0 [2024/04/12 07:18] (current) – [Process] wedge
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 =====OBJECTIVE===== =====OBJECTIVE=====
-To apply bitwise logic in the application of decoding IEEE754-encoded 32-bit values, displaying the decoded result.+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: 
 + 
 +  * https://en.wikipedia.org/wiki/IEEE_754 
 +  * https://www.puntoflotante.net/FLOATING-POINT-FORMAT-IEEE-754.htm 
 +  * [[https://www.sciencedirect.com/topics/engineering/floating-point-number#:~:text=The%20mantissa%20is%2023%20bits,%E2%88%923%20%3D%207%2F8.|sciencedirect]] 
 +  * https://www.h-schmidt.net/FloatConverter/IEEE754.html
  
 =====BACKGROUND===== =====BACKGROUND=====
-Much of our experience transacting in numbers on the computer has been with integer data. The format for unsigned data is straightforward.+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. Signed quantities undergo a process known as two's complement, which can be encoded/decoded to decipher the value stored within.
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 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. 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.
  
-{{:haas:fall2023:discrete:projects:ieee-754-english.jpg|}}+{{:haas:fall2023:discrete:projects:ieee754-binary-wikipedia.png|binary layout of IEEE754 (sourced from wikipedia article)}}
  
 ====Process==== ====Process====
-Walking through the decoding scheme, we'll start with an instance of IEEE754-encoded data: **C378C000**+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: 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:
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 ^  sign (bit 31)  ^  exponent (bits 30-23)  ^  mantissa (bits 22-0)  | ^  sign (bit 31)  ^  exponent (bits 30-23)  ^  mantissa (bits 22-0)  |
-|  1  |  100 0011 0  |  111 1000 1100 0000 0000 0000  |+|  1  |  <nowiki>100 0011 0</nowiki>  |  <nowiki>111 1000 1100 0000 0000 0000</nowiki>  |
  
 ===Determine the exponent=== ===Determine the exponent===
-In this example, we have **1000 0110** or **0x86** in our exponent section.+In this example, we have **<nowiki>1000 0110</nowiki>** 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: What we do now is take that value, and subtract a **0x7F** from it to get our actual exponent value:
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 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: 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+  * <nowiki>1 . 111 1000 1100 0000 0000 0000</nowiki>
  
 ===bit shift by exponent=== ===bit shift by exponent===
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 ===determine value to the left of the decimal point=== ===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**.+The value we have to the left of the decimal point is **<nowiki>11111000</nowiki>**, which when converted to decimal is **248**.
  
 We prefix the sign to this (1 indicates negative, which in this example it was), so: **-248.** We prefix the sign to this (1 indicates negative, which in this example it was), so: **-248.**
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 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. 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.+So, with our current value of **<nowiki>1100 0000 0000 0000</nowiki>**, we have exactly 2 values containing a 1. Positions 1 and 2.
  
 According to our formula: According to our formula:
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   * <nowiki>- 248 . 75</nowiki>   * <nowiki>- 248 . 75</nowiki>
  
-Therefore, **C378C000** decodes as **-248.75**+Therefore, **0xC378C000** decodes as **-248.75**
 =====TASK===== =====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. 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.
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 <code> <code>
-286:blf0:final tally of results (286/286) +52:blf0:final tally of results (52/52) 
-*:blf0:submitted C and assembly implementations [26/26] +*:blf0:implementation builds cleanly [13/13] 
-*:blf0:each implementation builds cleanly [26/26] +*:blf0:output conforms to specifications [13/13] 
-*:blf0:output conforms to specifications [26/26] +*:blf0:processing is correct, and to specifications [13/13] 
-*:blf0:processing is correct, and to specifications [26/26] +*:blf0:provided example worked through on documentation [13/13]
-*:blf0:working break on composite optimization [26/26] +
-*:blf0:working odds only processing optimization [26/26] +
-*:blf0:working sqrt factor cap optimization [26/26] +
-*:blf0:all variants and combinations thereof operational [26/26] +
-*:blf0:graph produced from timing data produced [26/26] +
-*:blf0:graph posted to discord and documentation page [26/26] +
-*:blf0:timing data is taken out to 3 decimal places [26/26]+
 </code> </code>
  
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   * 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 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   * 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
 +
haas/fall2023/discrete/projects/blf0.1712857650.txt.gz · Last modified: 2024/04/11 13:47 by wedge