Test Series

Question

How to get the second string,i.e., 6*2/1-2*3 from the given grammar?

Comments

is -7 the answer?

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in this grammar order of precedence is $/ > - >*$

division has the highest precedence
then minus 
then multiply but multiply is actually addition according to the rules defined

while solving a₁

(((8/4)+(2-6)+4) $\Rightarrow$ 2+(-4) + 4  

a₁ = 2

solving a₂

6+((2/1)-2)+3 $\Rightarrow$ 6+3 

a₂ = 9

$a _{1}- a_{2} = 2-9 = -7$

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Yes -7 is correct. Thanks for the explanation. I didn't take precedence into consideration.

Answer 1

More away from the Start symbol, Higher the precedence.

Here, $B\rightarrow C/b_{1}$ is 2 levels down from Start symbol

and $a\rightarrow A_{1} - B$ is 1 level away from start symbol, which clears that ' / ' has higher precedence than ' - ' and ' * '.

$So, / > - > *$

$a_{1} = 8/4 * 2 - 6*4; \\ = ( (8/4)*(2-6)*4);$

But as per first grammer, Multiplacation prints addition of two numbers. Therefore

$a_{1} = (2 + (-4) + 4) = 2;$

and, similarly $a_{2} = 6*2/1-2*3; \\ (6*((2/1)-2)*3); i.e. (6 +0 + 3) = 9$

Now, $a_{1} - a_{2} = 2 - 9 \\  = -7$