Step by Step solution about How to resolve the algorithm Variable-length quantity step by step in the Mathematica/Wolfram Language programming language

The provided Wolfram code handles conversions between integers and octet representations, where an octet is a sequence of eight bits.

toOctets[n]

• Converts an integer n into its octet representation as a string.
• It uses IntegerString to convert n to a hexadecimal string.
• It partitions the string into groups of two characters each.
• If the length of the string is odd, a leading "0" is added to the first group.
• The resulting groups (octets) are joined back together to form the octet representation.

fromOctets[octets]

• Reverses the toOctets process, converting a list of octets back into an integer.
• It joins all the octets into a single string.
• It converts the hexadecimal string to an integer using FromDigits.

Grid Usage

• The code demonstrates these functions by applying them to three different large integers: 16^^3ffffe, 16^^1fffff, and 16^^200000.
• It creates a grid where each row contains the integer, its octet representation, and the integer reconstructed from the octet representation.

Example: Say we have the integer 16^^3ffffe.

• toOctets[16^^3ffffe] gives {"03", "ff", "ff", "fe"} as the octet representation.
• fromOctets[{"03", "ff", "ff", "fe"}] successfully reconstructs the original integer 16^^3ffffe.

toOctets[n_Integer] := 
 StringJoin @@@ 
  Partition[
   PadLeft[Characters@IntegerString[n, 16], 
    2 Ceiling[Plus @@ DigitCount[n, 16]/2], {"0"}], 2]
fromOctets[octets_List] := FromDigits[StringJoin @@ octets, 16]
Grid[{#, toOctets@#, fromOctets[toOctets@#]} & /@ {16^^3ffffe, 16^^1fffff, 16^^200000}]