Recall that a floating$-$point number can be expressed as

$(-1{)}^s(1+f)2^e$

where $s,f$ and $e$ are binary numbers. Recall that $(s)$ is the sign indicator, $(f)$ the mantissa $($or fractional part$),$ and $(e)$ the exponent.

Suppose the sign is $1$ bit long, the mantissa $15$ bits long, and the exponent has $7$ bits. What are the largest and smallest positive numbers in this computer system?