To draw the parse tree and convert the binary number $"1101"$ into a decimal number using the given production rules and semantic rules, we can follow these steps:$1.$ Construct the Parse Tree: $-$ Start with the binary number: $"1101"-$ Apply the production rules to build the parse tree:$```$ S $|$ L $/\backslash$ L B $/\backslash$ L B $//$ L B $|$ B$```2.$ Convert the Binary Number to Decimal: $-$ Starting from the root of the parse tree $($top$-$down traversal$),$ apply the semantic rules to convert the binary number to decimal: $-$ Applying the semantic rules: $-\{$S$.$VAL :$=$ L$.$VAL$\}-\{$L$.$VAL :$=$ L$.$VAL $+$ B$.$VAL $*3\}-\{$L$.$VAL :$=$ B$.$VAL$\}-\{$B$.$VAL :$=0\}-\{$B$.$VAL :$=1\}-$ Convert the binary number: $-($S$.$VAL :$=1101)-($L$.$VAL :$=1101+1*3)-($L$.$VAL :$=1)-($B$.$VAL :$=1)-($B$.$VAL :$=0)-($B$.$VAL :$=1)-$ Final conversion: $-$ Binary Number: $1101-$ Decimal Number: $13$So$,$ the parse tree represents the structure of the binary number, and the conversion provides the decimal equivalent of the binary number according to the given rules. In this case, the binary number $"1101"$ is converted to the decimal number $13.$