CODE IN C Task $2$: String to number

In this task, you will ask the user for a string $x$ that represents a real number and the base $b$ in which this number iven. Your task is to convert this string in to the floating number in base $10.$

Note. Number in base $10$ are the numbers we use in our daily basis were all the number's digits are less than $10.$

Example:

$x=75\mathrm{.}32,b=8,$ Output:$61\mathrm{.}40625$

Explanation:

$-7*8^1=56$

$-5*8^0=5$

$-3*8^{-1}=0\mathrm{.}375$

$-2*8^{-2}=0\mathrm{.}03125$

Output: $56+5+0\mathrm{.}375+0\mathrm{.}03125=61\mathrm{.}40625$

$x=-75\mathrm{.}32,b=8,$ Output: $-61\mathrm{.}40625$

$1$

$x=101\mathrm{.}01,b=2,$ Output:$5\mathrm{.}25$

Explanation:

$-1*2^2=4$

$-0*2^1=0$

$-1*2^0=1$

$-0*2^{-1}=0$

$-1*2^{-2}=0\mathrm{.}25$

$-$ Output: $4+0+1+0+0\mathrm{.}25=5\mathrm{.}25$

$x=134\mathrm{.}51,b=5,$ Output: $0$

Explanation: The input is in base $5$ so all the digits must be less than

$5.$ Otherwise the input is wrong. In this cases, we return $0.$

Constraints: Consider the string will contain the following characters:

digits: $\text{'}0\text{'},\text{'}1\text{'},\text{'}2\text{'},\text{'}3\text{'},\text{'}4\text{'},\text{'}5\text{'},\text{'}6\text{'},\text{'}7\text{'},\text{'}8\text{'},\text{'}9\text{'}.$

symbols: $\text{'}-\text{'},\text{'},$

Subtasks:

Create a function to check if the given input is valid. Must finish in Lab

Create a function to convert a string into an positive integer. Assume that the input will not have decimal part and that it is positive. Must finish in Lab

Modify the previous function to include integer numbers. Assume that the input will not have decimal part. Must finish in Lab

Modify the previous function to include floating numbers.

Built$-$in functions are NOT allowed.