Converting a decimal to a mixed-radix (base) number

Question

How do you convert a decimal number to mixed radix notation?

I guess that given an input of an array of each of the bases, and the decimal number, it should output an array of the values of each column.

Answer 1

Pseudocode:

bases = [24, 60, 60]
input = 86462                       #One day, 1 hour, 2 seconds
output = []

for base in reverse(bases)
    output.prepend(input mod base)
    input = input div base          #div is integer division (round down)

Answer 2

Number -> set:

factors = [52,7,24,60,60,1000]
value = 662321
for i in n-1..0
  res[i] = value mod factors[i]
  value = value div factors[i]

And the reverse:

If you have the number like 32(52), 5(7), 7(24), 45(60), 15(60), 500(1000) and you want this converted to decimal:

Take number n, multiply it with the factor of n-1, continue for n-1..n=0

values = [32,5,7,45,15,500]
factors = [52,7,24,60,60,1000]

res = 0;
for i in 0..n-1
  res = res * factors[i] + values[i]

And you have the number.

Answer 3

I came up with a slightly different, and probably not as good method as the other ones here, but I thought I'd share anyway:

var theNumber = 313732097; 

//             ms   s   m   h    d
var bases = [1000, 60, 60, 24, 365];
var placeValues = [];  // initialise an array
var currPlaceValue = 1;

for (var i = 0, l = bases.length; i < l; ++i) {
    placeValues.push(currPlaceValue);
    currPlaceValue *= bases[i];
}
console.log(placeValues);
// this isn't relevant for this specific problem, but might
// be useful in related problems.
var maxNumber = currPlaceValue - 1;


var output = new Array(placeValues.length);

for (var v = placeValues.length - 1; v >= 0; --v) {
    output[v] = Math.floor(theNumber / placeValues[v]);
    theNumber %= placeValues[v];
}

console.log(output);
// [97, 52, 8, 15, 3] --> 3 days, 15 hours, 8 minutes, 52 seconds, 97 milliseconds