DOCUMENT();

loadMacros(
   "PGstandard.pl",     # Standard macros for PG language
   "MathObjects.pl",
   "PGML.pl",
   'nondecimal_base.pl',
   'contextArbitraryString.pl'
);

# The ArbitraryString context is used since numbers in bases > 10 are given in strings. 
# This context allows any string to be used in both the Compute and in student answers.

Context("ArbitraryString");



TEXT(beginproblem());
$a = random(30,50); $a_2 = Compute(convertBase($a, to => 2)); 
$b = random(30,50); $b_5 = Compute(convertBase($b, to => 5)); 
$c = random(70,100); $c_8 = Compute(convertBase($c, to => 8));
$d = random(115,150); $d_12 = Compute(convertBase($d, to => 12));
$e = random(150,250); $e_16 = Compute(convertBase($e, to => 16));

$aa = random(30,50); $aa_2 = Compute(convertBase($aa, to => 2));
$bb = random(30,50); $bb_5 = Compute(convertBase($bb, to => 5));
$cc = random(70,100); $cc_8 = Compute(convertBase($cc, to => 8));
$dd = random(100,150); $dd_12 = Compute(convertBase($dd, to => 12));
$ee = random(150,250); $ee_16 = Compute(convertBase($ee, to => 16));

$ff = random(100,200); $ff_12 = Compute(convertBase($ff, to => 12, digits => [0..9,'T','E']));
$gg = random(100,200); $gg_12 = Compute(convertBase($gg, to => 12, digits => [0..9,'T','E']));

BEGIN_PGML
Conver the following numbers in decimal to their value in the given bases:

1. [$a] = [__]{$a_2}[`_2`]
2. [$b] = [__]{$b_5}[`_5`]
3. [$c] = [__]{$c_8}[`_8`]
4. [$d] = [__]{$d_12}[`_{12}`]
5. [$e] = [__]{$e_16}[`_{16}`]

Convert the following numbers in the given base into it's decimal equivalent:

1. [$aa_2][`_2`] = [__]{$aa}
2. [$bb_5][`_5`] = [__]{$bb}
3. [$cc_8][`_8`] = [__]{$cc}
4. [$dd_12][`_{12}`] = [__]{$dd}
5. [$ee_16][`_{16}`] = [__]{$ee}

Convert the following numbers between decimal to base-12 using the digits T and E for ten and eleven.

1. [$ff_12][`_{12}`] = [__]{$ff}
2. [$gg] = [__]{$gg_12}[`_{12}`]

END_PGML

ENDDOCUMENT();