2^n calculator in pascal for n={bigger numbers} - pascal

Question

Before i must say this : Please, excuse me for my bad english...
I'm student.My teacher gave me problem in pascal for my course work...
I must write program that calculates 2^n for big values of n...I've wrote but there is a problem...My program returns 0 for values of n that bigger than 30...My code is below...Please help me:::Thanks beforehand...
function control(a: integer): boolean;
var
b: boolean;
begin
if (a >= 10) then b := true
else b := false;
control := b;
end;
const
n = 200000000;
var
a: array[1..n] of integer;
i, j, c, t, rsayi: longint; k: string;
begin
writeln('2^n');
write('n=');
read(k);
a[1] := 1;
rsayi := 1;
val(k, t, c);
for i := 1 to t do
for j := 1 to t div 2 do
begin
a[j] := a[j] * 2;
end;
for i := 1 to t div 2 do
begin
if control(a[j]) = true then
begin
a[j + 1] := a[j + 1] + (a[j] div 10);
a[j] := a[j] mod 10;
rsayi := rsayi + 1;
end;
end;
for j := rsayi downto 1 do write(a[j]);
end.

Answer 1

The first (nested) loop boils down to "t" multiplications by 2 on every single element of a.
30 multiplications by two is as far as you can go with a 32-bit integer (2^31-1 of positive values, so 2^31 is out of reach)
So the first loop doesn't work, and you probably have to rethink your strategy.

Answer 2

Here is a quick and dirty program to compute all 2^n up to some given, possibly large, n. The program repeatedly doubles the number in array a, which is stored in base 10; with lower digit in a[1]. Notice it's not particularly fast, so it would not be wise to use it for n = 200000000.
program powers;
const
n = 2000; { largest power to compute }
m = 700; { length of array, should be at least log(2)*n }
var
a: array[1 .. m] of integer;
carry, s, p, i, j: integer;
begin
p := 1;
a[1] := 1;
for i := 1 to n do
begin
carry := 0;
for j := 1 to p do
begin
s := 2*a[j] + carry;
if s >= 10 then
begin
carry := 1;
a[j] := s - 10
end
else
begin
carry := 0;
a[j] := s
end
end;
if carry > 0 then
begin
p := p + 1;
a[p] := 1
end;
write(i, ': ');
for j := p downto 1 do
write(a[j]);
writeln
end
end.