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Quinary to Binary converter

How to convert Quinary to Binary

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.

A binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically "0" and "1". The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices.


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

The simplest way is to convert the quinary number into decimal, then the decimal into binary form.
  1. Write the powers of 5 (1, 5, 25, 125, 625, and so on) beside the quinary digits from bottom to top.
  2. Multiply each digit by it's power.
  3. Add up the answers. This is the decimal solution.
  4. Divide the decimal number by 2.
  5. Get the integer quotient for the next iteration (if the number will not divide equally by 2, then round down the result to the nearest whole number).
  6. Keep a note of the remainder, it should be between 0 and 1.
  7. Repeat the steps from step 4. until the quotient is equal to 0.
  8. Write out all the remainders, from bottom to top. This is the binary solution.
For example if the given quinary number is 3012:
Then the decimal solution (375 + 5 + 2) is: 382
382 / 21910
191 / 2951
95 / 2471
47 / 2231
23 / 2111
11 / 251
5 / 221
2 / 210
1 / 201
Finally the binary solution is: 101111110
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