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Hex to Quinary converter

How to convert Hex to Quinary

Hexadecimal is a positional system that represents numbers using a base of 16. Unlike the common way of representing numbers with ten symbols, it uses sixteen distinct symbols, most often the symbols "0"-"9" to represent values zero to nine, and "A"-"F" to represent values ten to fifteen. Hexadecimal numerals are widely used by computer system designers and programmers, as they provide a human-friendly representation of binary-coded values.

Quinary is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand. In the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100 and sixty is written as 220.

Follow these steps to convert a hexadecimal number into quinary form:

The simplest way is to convert the hexadecimal number into decimal, then the decimal into quinary form.
  1. Write the powers of 16 (1, 16, 256, 4096, 65536, and so on) beside the hex digits from bottom to top.
  2. Convert any letters (A to F) to their corresponding numerical form.
  3. Multiply each digit by it's power.
  4. Add up the answers. This is the decimal solution.
  5. Divide the decimal number by 5.
  6. Get the integer quotient for the next iteration (if the number will not divide equally by 5, then round down the result to the nearest whole number).
  7. Keep a note of the remainder, it should be between 0 and 4.
  8. Repeat the steps from step 5. until the quotient is equal to 0.
  9. Write out all the remainders, from bottom to top. This is the quinary solution.
For example if the given hexadecimal number is A0E:
DigitPowerMultiplication
A (10)2562560
0160
E (14)114
Then the decimal solution (2560 + 14) is: 2574
DivisionQuotientRemainder
2574 / 55144
514 / 51024
102 / 5202
20 / 540
4 / 504
Finally the quinary solution is: 40244
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