Find a grammar that generates numbers with the following

requirements:

$($a$)$ a number may be signed $($with $+$ or $-$ symbol$)$ or unsigned.

$($b$)$ the value field consists of two nonempty parts, separated by a

decimal point.

$($c$)$ there is an optional exponent field. If present, this field must contain

the letter e$,$ followed by a signed two$-$digit integer.

For example, $+12\mathrm{.}25,0\mathrm{.}125,-20\mathrm{.}45e+10,$ and $35\mathrm{.}1e-02$ are all legal

numbers.