Processors

_posts/2022-07-19-processors.markdown

@@ -70,9 +70,9 @@ We can see from above that the size of the word, loosely depends on
 
 1. How many bits are required to encode the smallest human readable alphabet? When dealing with arithmetic on very large numbers, we would need more than 8 bits (it is often 32 or 64 bits)
 
-1. How much memory is required to be addressable to run any programmed application? In general, the size of RAM usable by a processor = *2<sup>word-size</sup>* in bytes.
+1. How much memory is required to be addressable to run any programmed application? In general, the size of RAM usable by a processor = *2^word-size* in bytes.
 
-> RAM usable by a processor = *2<sup>word-size</sup>* in bytes
+> RAM usable by a processor = *2^word-size* in bytes
 
 # What does all these have to do with the original question?
 
@@ -80,11 +80,11 @@ What does 64 mean in a 64-bit processor?
 
 For a 64-bit procesor, the word size that a processor operates in, is (*begin drum rolls....*) **64** (*end drum rolls*)
 
-We started with 8-bit processor in the 1970s. Commodity computers now all have 64-bit processors now. We made the shift from 32 bit to 64 bit over the last decade. 32 bits are already too much to distinguish alphabets and dealing with large numbers (32 bits can already differentiate 10<sup>9</sup> things. 64 bits can differentiate 10<sup>19</sup> things).
+We started with 8-bit processor in the 1970s. Commodity computers now all have 64-bit processors now. We made the shift from 32 bit to 64 bit over the last decade. 32 bits are already too much to distinguish alphabets and dealing with large numbers (32 bits can already differentiate 10^9 things. 64 bits can differentiate 10^19 things).
 
 The reason we went from 32 to 64 in the first place is not because we had a large alphabet set, or we wanted to work with large numbers. It was simply because the programs running on the computer needed a lot of addressable memory.
 
-- 2<sup>32</sup> = 4GB
+- 2^32 = 4GB
 
 A 32-bit processor cannot use up more than 4GB of RAM.
 
@@ -92,7 +92,7 @@ We've come up with a lot of memory heavy programs now - video games, video proce
 
 Recall that computers work well with powers of 2. So instead of a 33-bit computer, the next processor type is instead a 64-bit processor.
 
-- 2<sup>64</sup> = 20 quadrillion GB.
+- 2^64 = 20 quadrillion GB.
 
 That's how exponents work! The answer should be pretty clear now - we probably don't have that many 'things' to distinguish and address.
 
@@ -102,5 +102,5 @@ We don't need a 128 bit processor!!
 
 When the human race is captured by the robot overlords, they might want to map every particle in the known universe which is around 7 octillion, and hold everything in the RAM for real time tracking.
 
-But that only uses up 92 of the 128 bits. (2<sup>92</sup> is around 7 octillion). They can use the remaining 38 bits to map the particles in alternate universes. 38 bits can address 10 billion things. This **SUPER COMPUTER** can therefore be used to track all the particles in 10 billion universes.
+But that only uses up 92 of the 128 bits. (2^92 is around 7 octillion). They can use the remaining 38 bits to map the particles in alternate universes. 38 bits can address 10 billion things. This **SUPER COMPUTER** can therefore be used to track all the particles in 10 billion universes.
 

index.html

@@ -46,4 +46,4 @@ layout: default
     {% endif %}
   </div>
   {% endif %}
-</div>
+</div>