For the following number: $64,323$

$[$Syntax$]$ Write down the Parse Tree for this number using the following rules:

$[$Semantics$]$ Prove the calculation of this number using the following rules:

The denotational mappings for these syntax rules are

$M_{\text{d}\text{e}\text{c}}{(}^{\text{'}}{0}^{\text{'}})=0,M_{\text{d}\text{e}\text{c}}(1^{\text{'}})=1,M_{\text{d}\text{e}\text{c}}(2^{\text{'}})=2,$dots,$M_{\text{d}\text{e}\text{c}}{(}^{\text{'}}{9}^{\text{'}})=9$

Write the Grammar Rules and Denotational Mappings for a Hexadecimal System.

Then:

come a four$-$digit hexadecimal number using the extra characters

write the parse tree for what you came up with

prove its value using denotational semantics.